diff --git a/Makefile b/Makefile
index eb3020e34..aa088a11e 100644
--- a/Makefile
+++ b/Makefile
@@ -395,6 +395,17 @@ AUTO_SOURCES_CS_TARGETS=$(subst .spthy,_analyzed-auto-sources.spthy,$(addprefix
 auto-sources-case-studies:	$(AUTO_SOURCES_CS_TARGETS)
 	grep "verified\|falsified\|processing time" case-studies$(SUBDIR)features/auto-sources/spore/*.spthy
 
+## Accountability
+################
+
+ACCOUNTABILITY_CASE_STUDIES=ct.spthy whodunit.spthy ocsps-msr.spthy ocsps-msr-untrusted.spthy
+
+ACCOUNTABILITY_CS_TARGETS=$(subst .spthy,_analyzed.spthy,$(addprefix case-studies$(SUBDIR)accountability/csf21-acc-unbounded/previous/,$(ACCOUNTABILITY_CASE_STUDIES)))
+
+# case studies
+accountability-case-studies:	$(ACCOUNTABILITY_CS_TARGETS)
+	grep "verified\|falsified\|processing time" case-studies$(SUBDIR)accountability/csf21-acc-unbounded/previous/*.spthy
+
 ## Regression (old issues)
 ##########################
 
@@ -456,7 +467,7 @@ else 	# ($(UNAME_S),Darwin)
 endif
 #	top -b | head >> $@
 
-CS_TARGETS=case-studies$(SUBDIR)Tutorial_analyzed.spthy $(CSF19_WRAPPING_TARGETS) $(CSF12_CS_TARGETS) $(CLASSIC_CS_TARGETS) $(IND_CS_TARGETS) $(AKE_DH_CS_TARGETS) $(AKE_BP_CS_TARGETS) $(FEATURES_CS_TARGETS) $(OBSEQ_TARGETS) $(SAPIC_CS_TARGETS_FAST) $(SAPIC_CS_TARGETS_SLOW) $(POST17_TARGETS) $(REGRESSION_TARGETS) $(XOR_TARGETS) $(AUTO_SOURCES_CS_TARGETS)
+CS_TARGETS=case-studies$(SUBDIR)Tutorial_analyzed.spthy $(CSF19_WRAPPING_TARGETS) $(CSF12_CS_TARGETS) $(CLASSIC_CS_TARGETS) $(IND_CS_TARGETS) $(AKE_DH_CS_TARGETS) $(AKE_BP_CS_TARGETS) $(FEATURES_CS_TARGETS) $(OBSEQ_TARGETS) $(SAPIC_CS_TARGETS_FAST) $(SAPIC_CS_TARGETS_SLOW) $(POST17_TARGETS) $(REGRESSION_TARGETS) $(XOR_TARGETS) $(AUTO_SOURCES_CS_TARGETS) $(ACCOUNTABILITY_CS_TARGETS)
 
 case-studies: 	case-studies$(SUBDIR)system.info $(CS_TARGETS)
 	grep -R "verified\|falsified\|processing time" case-studies$(SUBDIR)
diff --git a/case-studies-regression/accountability/csf21-acc-unbounded/previous/ct_analyzed.spthy b/case-studies-regression/accountability/csf21-acc-unbounded/previous/ct_analyzed.spthy
new file mode 100644
index 000000000..d16500124
--- /dev/null
+++ b/case-studies-regression/accountability/csf21-acc-unbounded/previous/ct_analyzed.spthy
@@ -0,0 +1,5700 @@
+theory CertificateTransparencyExt begin
+
+// Function signature and definition of the equational theory E
+
+functions: fst/1, pair/2, pk/1, read/1, sign/2,
+           skca/1[private,destructor], snd/1, true/0, verify/3
+equations:
+    fst(<x.1, x.2>) = x.1,
+    read(sign(sk, m)) = m,
+    snd(<x.1, x.2>) = x.2,
+    verify(sign(sk, m), m, pk(sk)) = true
+
+
+
+heuristic: p
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+restriction terminate:
+  "∃ #t. Terminate( ) @ #t"
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+rule (modulo E) inca_0_1111111[color=#408053, process="in($ca.1);"]:
+   [ State_1111111( ), In( $ca.1 ) ]
+  -->
+   [ !Semistate_11111111111( $ca.1 ), Out( pk(skca($ca.1)) ) ]
+
+  /*
+  rule (modulo AC) inca_0_1111111[color=#408053, process="in($ca.1);"]:
+     [ State_1111111( ), In( $ca ) ]
+    -->
+     [ !Semistate_11111111111( $ca ), Out( pk(skca($ca)) ) ]
+  */
+
+rule (modulo E) p_1_1111111111[color=#40806c, process="!"]:
+   [ !Semistate_11111111111( $ca.1 ), In( <$s.1, $ca.2> ), Fr( skS.1 ) ]
+  --[ HonestRegister( $s.1, $ca.2, pk(skS.1) ) ]->
+   [ State_11111111111111( $ca.1, $s.1, skS.1, $ca.2 ) ]
+
+  /*
+  rule (modulo AC) p_1_1111111111[color=#40806c, process="!"]:
+     [ !Semistate_11111111111( $ca ), In( <$s, $ca.1> ), Fr( skS ) ]
+    --[ HonestRegister( $s, $ca.1, pk(skS) ) ]->
+     [ State_11111111111111( $ca, $s, skS, $ca.1 ) ]
+  */
+
+rule (modulo E) insertcaproofOfIDspkskSyes_0_11111111111111[color=#40806c,
+                                                            process="insert <$ca.2, 'proofOfID', $s.1, pk(skS.1)>,'yes';"]:
+   [ State_11111111111111( $ca.1, $s.1, skS.1, $ca.2 ) ]
+  --[ Insert( <$ca.2, 'proofOfID', $s.1, pk(skS.1)>, 'yes' ) ]->
+   [ State_1111111111111111( $ca.1, $s.1, skS.1, $ca.2 ), Out( pk(skS.1) ) ]
+
+  /*
+  rule (modulo AC) insertcaproofOfIDspkskSyes_0_11111111111111[color=#40806c,
+                                                               process="insert <$ca.2, 'proofOfID', $s.1, pk(skS.1)>,'yes';"]:
+     [ State_11111111111111( $ca, $s, skS, $ca.1 ) ]
+    --[ Insert( <$ca.1, 'proofOfID', $s, pk(skS)>, 'yes' ) ]->
+     [ State_1111111111111111( $ca, $s, skS, $ca.1 ), Out( pk(skS) ) ]
+  */
+
+rule (modulo E) outsignskcacapkskSs_0_1111111111111111[color=#40806c,
+                                                       process="out(sign(skca($ca.2), <pk(skS.1), $s.1>));"]:
+   [ State_1111111111111111( $ca.1, $s.1, skS.1, $ca.2 ) ]
+  -->
+   [ Out( sign(skca($ca.2), <pk(skS.1), $s.1>) ) ]
+
+  /*
+  rule (modulo AC) outsignskcacapkskSs_0_1111111111111111[color=#40806c,
+                                                          process="out(sign(skca($ca.2), <pk(skS.1), $s.1>));"]:
+     [ State_1111111111111111( $ca, $s, skS, $ca.1 ) ]
+    -->
+     [ Out( sign(skca($ca.1), <pk(skS), $s>) ) ]
+  */
+
+rule (modulo E) inla_0_1111112[color=#408053, process="in($la.1);"]:
+   [ State_1111112( ), In( $la.1 ), In( sign(skca($ca.3), <pk.1, $s.2>) ) ]
+  -->
+   [ !Semistate_11111121111( $la.1, pk.1, $s.2, $ca.3 ) ]
+
+  /*
+  rule (modulo AC) inla_0_1111112[color=#408053, process="in($la.1);"]:
+     [ State_1111112( ), In( $la ), In( sign(skca($ca), <pk, $s>) ) ]
+    -->
+     [ !Semistate_11111121111( $la, pk, $s, $ca ) ]
+  */
+
+rule (modulo E) p_1_1111112111[color=#408069, process="!"]:
+   [ !Semistate_11111121111( $la.1, pk.1, $s.2, $ca.3 ), Fr( lock ) ]
+  --[ Lock_0( '0', lock, 'log' ), Lock( '0', lock, 'log' ) ]->
+   [ State_111111211111( lock, $la.1, pk.1, $s.2, $ca.3 ) ]
+
+  /*
+  rule (modulo AC) p_1_1111112111[color=#408069, process="!"]:
+     [ !Semistate_11111121111( $la, pk, $s, $ca ), Fr( lock ) ]
+    --[ Lock_0( '0', lock, 'log' ), Lock( '0', lock, 'log' ) ]->
+     [ State_111111211111( lock, $la, pk, $s, $ca ) ]
+  */
+
+rule (modulo E) insertlalogspkcyes_0_111111211111[color=#408069,
+                                                  process="insert <$la.1, 'log', $s.2, pk.1, 'c1'>,'yes';"]:
+   [ State_111111211111( lock, $la.1, pk.1, $s.2, $ca.3 ) ]
+  --[ Insert( <$la.1, 'log', $s.2, pk.1, 'c1'>, 'yes' ) ]->
+   [ State_1111112111111( lock, $la.1, pk.1, $s.2, $ca.3 ) ]
+
+  /*
+  rule (modulo AC) insertlalogspkcyes_0_111111211111[color=#408069,
+                                                     process="insert <$la.1, 'log', $s.2, pk.1, 'c1'>,'yes';"]:
+     [ State_111111211111( lock, $la, pk, $s, $ca ) ]
+    --[ Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) ]->
+     [ State_1111112111111( lock, $la, pk, $s, $ca ) ]
+  */
+
+rule (modulo E) insertlalogspksyes_0_1111112111111[color=#408069,
+                                                   process="insert <$la.1, 'log', $s.2, pk.1, 's1'>,'yes';"]:
+   [ State_1111112111111( lock, $la.1, pk.1, $s.2, $ca.3 ) ]
+  --[ Insert( <$la.1, 'log', $s.2, pk.1, 's1'>, 'yes' ) ]->
+   [ State_11111121111111( lock, $la.1, pk.1, $s.2, $ca.3 ) ]
+
+  /*
+  rule (modulo AC) insertlalogspksyes_0_1111112111111[color=#408069,
+                                                      process="insert <$la.1, 'log', $s.2, pk.1, 's1'>,'yes';"]:
+     [ State_1111112111111( lock, $la, pk, $s, $ca ) ]
+    --[ Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) ]->
+     [ State_11111121111111( lock, $la, pk, $s, $ca ) ]
+  */
+
+rule (modulo E) insertlalogspkiyes_0_11111121111111[color=#408069,
+                                                    process="insert <$la.1, 'log', $s.2, pk.1, 'i'>,'yes';"]:
+   [ State_11111121111111( lock, $la.1, pk.1, $s.2, $ca.3 ) ]
+  --[ Insert( <$la.1, 'log', $s.2, pk.1, 'i'>, 'yes' ) ]->
+   [ State_111111211111111( lock, $la.1, pk.1, $s.2, $ca.3 ) ]
+
+  /*
+  rule (modulo AC) insertlalogspkiyes_0_11111121111111[color=#408069,
+                                                       process="insert <$la.1, 'log', $s.2, pk.1, 'i'>,'yes';"]:
+     [ State_11111121111111( lock, $la, pk, $s, $ca ) ]
+    --[ Insert( <$la, 'log', $s, pk, 'i'>, 'yes' ) ]->
+     [ State_111111211111111( lock, $la, pk, $s, $ca ) ]
+  */
+
+rule (modulo E) unlocklog_0_111111211111111[color=#408069,
+                                            process="unlock 'log';"]:
+   [ State_111111211111111( lock, $la.1, pk.1, $s.2, $ca.3 ) ]
+  --[ Unlock_0( '0', lock, 'log' ), Unlock( '0', lock, 'log' ) ]->
+   [ ]
+
+  /*
+  rule (modulo AC) unlocklog_0_111111211111111[color=#408069,
+                                               process="unlock 'log';"]:
+     [ State_111111211111111( lock, $la, pk, $s, $ca ) ]
+    --[ Unlock_0( '0', lock, 'log' ), Unlock( '0', lock, 'log' ) ]->
+     [ ]
+  */
+
+rule (modulo E) locktestCA_0_1111121[color=#408069,
+                                     process="lock 'testCA';"]:
+   [ State_1111121( ), Fr( lock.1 ), In( sign(skca($ca.4), <pk.2, $s.3>) ) ]
+  --[ Lock_1( '1', lock.1, 'testCA' ), Lock( '1', lock.1, 'testCA' ) ]->
+   [ State_111112111( lock.1, pk.2, $s.3, $ca.4 ) ]
+
+  /*
+  rule (modulo AC) locktestCA_0_1111121[color=#408069,
+                                        process="lock 'testCA';"]:
+     [ State_1111121( ), Fr( lock ), In( sign(skca($ca), <pk, $s>) ) ]
+    --[ Lock_1( '1', lock, 'testCA' ), Lock( '1', lock, 'testCA' ) ]->
+     [ State_111112111( lock, pk, $s, $ca ) ]
+  */
+
+rule (modulo E) lookupcaproofOfIDspkasignored_0_111112111[color=#408080,
+                                                          process="lookup <$ca.4, 'proofOfID', $s.3, pk.2> as ignored.1"]:
+   [ State_111112111( lock.1, pk.2, $s.3, $ca.4 ) ]
+  --[ IsIn( <$ca.4, 'proofOfID', $s.3, pk.2>, ignored.1 ) ]->
+   [ State_1111121111( ignored.1, lock.1, pk.2, $s.3, $ca.4 ) ]
+
+  /*
+  rule (modulo AC) lookupcaproofOfIDspkasignored_0_111112111[color=#408080,
+                                                             process="lookup <$ca.4, 'proofOfID', $s.3, pk.2> as ignored.1"]:
+     [ State_111112111( lock, pk, $s, $ca ) ]
+    --[ IsIn( <$ca, 'proofOfID', $s, pk>, ignored ) ]->
+     [ State_1111121111( ignored, lock, pk, $s, $ca ) ]
+  */
+
+rule (modulo E) eventHonestCAca_0_1111121111[color=#408080,
+                                             process="event HonestCA( $ca.4 );"]:
+   [ State_1111121111( ignored.1, lock.1, pk.2, $s.3, $ca.4 ) ]
+  --[ HonestCA( $ca.4 ) ]->
+   [ State_11111211111( ignored.1, lock.1, pk.2, $s.3, $ca.4 ) ]
+
+  /*
+  rule (modulo AC) eventHonestCAca_0_1111121111[color=#408080,
+                                                process="event HonestCA( $ca.4 );"]:
+     [ State_1111121111( ignored, lock, pk, $s, $ca ) ]
+    --[ HonestCA( $ca ) ]->
+     [ State_11111211111( ignored, lock, pk, $s, $ca ) ]
+  */
+
+rule (modulo E) eventTestCAcaspk_0_11111211111[color=#408080,
+                                               process="event TestCA( $ca.4, $s.3, pk.2 );"]:
+   [ State_11111211111( ignored.1, lock.1, pk.2, $s.3, $ca.4 ) ]
+  --[ TestCA( $ca.4, $s.3, pk.2 ) ]->
+   [ State_111112111111( ignored.1, lock.1, pk.2, $s.3, $ca.4 ) ]
+
+  /*
+  rule (modulo AC) eventTestCAcaspk_0_11111211111[color=#408080,
+                                                  process="event TestCA( $ca.4, $s.3, pk.2 );"]:
+     [ State_11111211111( ignored, lock, pk, $s, $ca ) ]
+    --[ TestCA( $ca, $s, pk ) ]->
+     [ State_111112111111( ignored, lock, pk, $s, $ca ) ]
+  */
+
+rule (modulo E) unlocktestCA_0_111112111111[color=#408080,
+                                            process="unlock 'testCA';"]:
+   [ State_111112111111( ignored.1, lock.1, pk.2, $s.3, $ca.4 ) ]
+  --[ Unlock_1( '1', lock.1, 'testCA' ), Unlock( '1', lock.1, 'testCA' )
+  ]->
+   [ ]
+
+  /*
+  rule (modulo AC) unlocktestCA_0_111112111111[color=#408080,
+                                               process="unlock 'testCA';"]:
+     [ State_111112111111( ignored, lock, pk, $s, $ca ) ]
+    --[ Unlock_1( '1', lock, 'testCA' ), Unlock( '1', lock, 'testCA' ) ]->
+     [ ]
+  */
+
+rule (modulo E) lookupcaproofOfIDspkasignored_1_111112111[color=#408080,
+                                                          process="lookup <$ca.4, 'proofOfID', $s.3, pk.2> as ignored.1"]:
+   [ State_111112111( lock.1, pk.2, $s.3, $ca.4 ) ]
+  --[ IsNotSet( <$ca.4, 'proofOfID', $s.3, pk.2> ) ]->
+   [ State_1111121112( lock.1, pk.2, $s.3, $ca.4 ) ]
+
+  /*
+  rule (modulo AC) lookupcaproofOfIDspkasignored_1_111112111[color=#408080,
+                                                             process="lookup <$ca.4, 'proofOfID', $s.3, pk.2> as ignored.1"]:
+     [ State_111112111( lock, pk, $s, $ca ) ]
+    --[ IsNotSet( <$ca, 'proofOfID', $s, pk> ) ]->
+     [ State_1111121112( lock, pk, $s, $ca ) ]
+  */
+
+rule (modulo E) eventDishonestCAca_0_1111121112[color=#408080,
+                                                process="event DishonestCA( $ca.4 );"]:
+   [ State_1111121112( lock.1, pk.2, $s.3, $ca.4 ) ]
+  --[ DishonestCA( $ca.4 ) ]->
+   [ State_11111211121( lock.1, pk.2, $s.3, $ca.4 ) ]
+
+  /*
+  rule (modulo AC) eventDishonestCAca_0_1111121112[color=#408080,
+                                                   process="event DishonestCA( $ca.4 );"]:
+     [ State_1111121112( lock, pk, $s, $ca ) ]
+    --[ DishonestCA( $ca ) ]->
+     [ State_11111211121( lock, pk, $s, $ca ) ]
+  */
+
+rule (modulo E) eventTestCAcaspk_0_11111211121[color=#408080,
+                                               process="event TestCA( $ca.4, $s.3, pk.2 );"]:
+   [ State_11111211121( lock.1, pk.2, $s.3, $ca.4 ) ]
+  --[ TestCA( $ca.4, $s.3, pk.2 ) ]->
+   [ State_111112111211( lock.1, pk.2, $s.3, $ca.4 ) ]
+
+  /*
+  rule (modulo AC) eventTestCAcaspk_0_11111211121[color=#408080,
+                                                  process="event TestCA( $ca.4, $s.3, pk.2 );"]:
+     [ State_11111211121( lock, pk, $s, $ca ) ]
+    --[ TestCA( $ca, $s, pk ) ]->
+     [ State_111112111211( lock, pk, $s, $ca ) ]
+  */
+
+rule (modulo E) unlocktestCA_0_111112111211[color=#408080,
+                                            process="unlock 'testCA';"]:
+   [ State_111112111211( lock.1, pk.2, $s.3, $ca.4 ) ]
+  --[ Unlock_1( '1', lock.1, 'testCA' ), Unlock( '1', lock.1, 'testCA' )
+  ]->
+   [ ]
+
+  /*
+  rule (modulo AC) unlocktestCA_0_111112111211[color=#408080,
+                                               process="unlock 'testCA';"]:
+     [ State_111112111211( lock, pk, $s, $ca ) ]
+    --[ Unlock_1( '1', lock, 'testCA' ), Unlock( '1', lock, 'testCA' ) ]->
+     [ ]
+  */
+
+rule (modulo E) locklog_0_111121[color=#40805d, process="lock 'log';"]:
+   [ State_111121( ), Fr( lock.2 ), In( <$la.2, 'c1', 's1', $s.4, pk.3> ) ]
+  --[ Lock_2( '2', lock.2, 'log' ), Lock( '2', lock.2, 'log' ) ]->
+   [ State_11112111( $la.2, lock.2, pk.3, $s.4 ) ]
+
+  /*
+  rule (modulo AC) locklog_0_111121[color=#40805d, process="lock 'log';"]:
+     [ State_111121( ), Fr( lock ), In( <$la, 'c1', 's1', $s, pk> ) ]
+    --[ Lock_2( '2', lock, 'log' ), Lock( '2', lock, 'log' ) ]->
+     [ State_11112111( $la, lock, pk, $s ) ]
+  */
+
+rule (modulo E) lookuplalogspkcasx_0_11112111[color=#408067,
+                                              process="lookup <$la.2, 'log', $s.4, pk.3, 'c1'> as x1.1"]:
+   [ State_11112111( $la.2, lock.2, pk.3, $s.4 ) ]
+  --[ IsIn( <$la.2, 'log', $s.4, pk.3, 'c1'>, x1.1 ) ]->
+   [ State_111121111( x1.1, $la.2, lock.2, pk.3, $s.4 ) ]
+
+  /*
+  rule (modulo AC) lookuplalogspkcasx_0_11112111[color=#408067,
+                                                 process="lookup <$la.2, 'log', $s.4, pk.3, 'c1'> as x1.1"]:
+     [ State_11112111( $la, lock, pk, $s ) ]
+    --[ IsIn( <$la, 'log', $s, pk, 'c1'>, x1 ) ]->
+     [ State_111121111( x1, $la, lock, pk, $s ) ]
+  */
+
+rule (modulo E) lookuplalogspksasx_0_111121111[color=#408067,
+                                               process="lookup <$la.2, 'log', $s.4, pk.3, 's1'> as x2.1"]:
+   [ State_111121111( x1.1, $la.2, lock.2, pk.3, $s.4 ) ]
+  --[ IsIn( <$la.2, 'log', $s.4, pk.3, 's1'>, x2.1 ) ]->
+   [ State_1111211111( x1.1, x2.1, $la.2, lock.2, pk.3, $s.4 ) ]
+
+  /*
+  rule (modulo AC) lookuplalogspksasx_0_111121111[color=#408067,
+                                                  process="lookup <$la.2, 'log', $s.4, pk.3, 's1'> as x2.1"]:
+     [ State_111121111( x1, $la, lock, pk, $s ) ]
+    --[ IsIn( <$la, 'log', $s, pk, 's1'>, x2 ) ]->
+     [ State_1111211111( x1, x2, $la, lock, pk, $s ) ]
+  */
+
+rule (modulo E) eventHonestLA_0_1111211111[color=#408067,
+                                           process="event HonestLA( );"]:
+   [ State_1111211111( x1.1, x2.1, $la.2, lock.2, pk.3, $s.4 ) ]
+  --[ HonestLA( ) ]->
+   [ State_11112111111( x1.1, x2.1, $la.2, lock.2, pk.3, $s.4 ) ]
+
+  /*
+  rule (modulo AC) eventHonestLA_0_1111211111[color=#408067,
+                                              process="event HonestLA( );"]:
+     [ State_1111211111( x1, x2, $la, lock, pk, $s ) ]
+    --[ HonestLA( ) ]->
+     [ State_11112111111( x1, x2, $la, lock, pk, $s ) ]
+  */
+
+rule (modulo E) eventTestLAlaspk_0_11112111111[color=#408067,
+                                               process="event TestLA( $la.2, $s.4, pk.3 );"]:
+   [ State_11112111111( x1.1, x2.1, $la.2, lock.2, pk.3, $s.4 ) ]
+  --[ TestLA( $la.2, $s.4, pk.3 ) ]->
+   [ State_111121111111( x1.1, x2.1, $la.2, lock.2, pk.3, $s.4 ) ]
+
+  /*
+  rule (modulo AC) eventTestLAlaspk_0_11112111111[color=#408067,
+                                                  process="event TestLA( $la.2, $s.4, pk.3 );"]:
+     [ State_11112111111( x1, x2, $la, lock, pk, $s ) ]
+    --[ TestLA( $la, $s, pk ) ]->
+     [ State_111121111111( x1, x2, $la, lock, pk, $s ) ]
+  */
+
+rule (modulo E) unlocklog_0_111121111111[color=#408067,
+                                         process="unlock 'log';"]:
+   [ State_111121111111( x1.1, x2.1, $la.2, lock.2, pk.3, $s.4 ) ]
+  --[ Unlock_2( '2', lock.2, 'log' ), Unlock( '2', lock.2, 'log' ) ]->
+   [ ]
+
+  /*
+  rule (modulo AC) unlocklog_0_111121111111[color=#408067,
+                                            process="unlock 'log';"]:
+     [ State_111121111111( x1, x2, $la, lock, pk, $s ) ]
+    --[ Unlock_2( '2', lock, 'log' ), Unlock( '2', lock, 'log' ) ]->
+     [ ]
+  */
+
+rule (modulo E) lookuplalogspksasx_1_111121111[color=#408067,
+                                               process="lookup <$la.2, 'log', $s.4, pk.3, 's1'> as x2.1"]:
+   [ State_111121111( x1.1, $la.2, lock.2, pk.3, $s.4 ) ]
+  --[ IsNotSet( <$la.2, 'log', $s.4, pk.3, 's1'> ) ]->
+   [ State_1111211112( x1.1, $la.2, lock.2, pk.3, $s.4 ) ]
+
+  /*
+  rule (modulo AC) lookuplalogspksasx_1_111121111[color=#408067,
+                                                  process="lookup <$la.2, 'log', $s.4, pk.3, 's1'> as x2.1"]:
+     [ State_111121111( x1, $la, lock, pk, $s ) ]
+    --[ IsNotSet( <$la, 'log', $s, pk, 's1'> ) ]->
+     [ State_1111211112( x1, $la, lock, pk, $s ) ]
+  */
+
+rule (modulo E) eventDishonestLAla_0_1111211112[color=#408067,
+                                                process="event DishonestLA( $la.2 );"]:
+   [ State_1111211112( x1.1, $la.2, lock.2, pk.3, $s.4 ) ]
+  --[ DishonestLA( $la.2 ) ]->
+   [ State_11112111121( x1.1, $la.2, lock.2, pk.3, $s.4 ) ]
+
+  /*
+  rule (modulo AC) eventDishonestLAla_0_1111211112[color=#408067,
+                                                   process="event DishonestLA( $la.2 );"]:
+     [ State_1111211112( x1, $la, lock, pk, $s ) ]
+    --[ DishonestLA( $la ) ]->
+     [ State_11112111121( x1, $la, lock, pk, $s ) ]
+  */
+
+rule (modulo E) eventTestLAlaspk_0_11112111121[color=#408067,
+                                               process="event TestLA( $la.2, $s.4, pk.3 );"]:
+   [ State_11112111121( x1.1, $la.2, lock.2, pk.3, $s.4 ) ]
+  --[ TestLA( $la.2, $s.4, pk.3 ) ]->
+   [ State_111121111211( x1.1, $la.2, lock.2, pk.3, $s.4 ) ]
+
+  /*
+  rule (modulo AC) eventTestLAlaspk_0_11112111121[color=#408067,
+                                                  process="event TestLA( $la.2, $s.4, pk.3 );"]:
+     [ State_11112111121( x1, $la, lock, pk, $s ) ]
+    --[ TestLA( $la, $s, pk ) ]->
+     [ State_111121111211( x1, $la, lock, pk, $s ) ]
+  */
+
+rule (modulo E) unlocklog_0_111121111211[color=#408067,
+                                         process="unlock 'log';"]:
+   [ State_111121111211( x1.1, $la.2, lock.2, pk.3, $s.4 ) ]
+  --[ Unlock_2( '2', lock.2, 'log' ), Unlock( '2', lock.2, 'log' ) ]->
+   [ ]
+
+  /*
+  rule (modulo AC) unlocklog_0_111121111211[color=#408067,
+                                            process="unlock 'log';"]:
+     [ State_111121111211( x1, $la, lock, pk, $s ) ]
+    --[ Unlock_2( '2', lock, 'log' ), Unlock( '2', lock, 'log' ) ]->
+     [ ]
+  */
+
+rule (modulo E) lookuplalogspkcasx_1_11112111[color=#408067,
+                                              process="lookup <$la.2, 'log', $s.4, pk.3, 'c1'> as x1.1"]:
+   [ State_11112111( $la.2, lock.2, pk.3, $s.4 ) ]
+  --[ IsNotSet( <$la.2, 'log', $s.4, pk.3, 'c1'> ) ]->
+   [ State_111121112( $la.2, lock.2, pk.3, $s.4 ) ]
+
+  /*
+  rule (modulo AC) lookuplalogspkcasx_1_11112111[color=#408067,
+                                                 process="lookup <$la.2, 'log', $s.4, pk.3, 'c1'> as x1.1"]:
+     [ State_11112111( $la, lock, pk, $s ) ]
+    --[ IsNotSet( <$la, 'log', $s, pk, 'c1'> ) ]->
+     [ State_111121112( $la, lock, pk, $s ) ]
+  */
+
+rule (modulo E) lookuplalogspksasx_0_111121112[color=#408067,
+                                               process="lookup <$la.2, 'log', $s.4, pk.3, 's1'> as x2.2"]:
+   [ State_111121112( $la.2, lock.2, pk.3, $s.4 ) ]
+  --[ IsIn( <$la.2, 'log', $s.4, pk.3, 's1'>, x2.2 ) ]->
+   [ State_1111211121( $la.2, lock.2, x2.2, pk.3, $s.4 ) ]
+
+  /*
+  rule (modulo AC) lookuplalogspksasx_0_111121112[color=#408067,
+                                                  process="lookup <$la.2, 'log', $s.4, pk.3, 's1'> as x2.2"]:
+     [ State_111121112( $la, lock, pk, $s ) ]
+    --[ IsIn( <$la, 'log', $s, pk, 's1'>, x2 ) ]->
+     [ State_1111211121( $la, lock, x2, pk, $s ) ]
+  */
+
+rule (modulo E) eventDishonestLAla_0_1111211121[color=#408067,
+                                                process="event DishonestLA( $la.2 );"]:
+   [ State_1111211121( $la.2, lock.2, x2.2, pk.3, $s.4 ) ]
+  --[ DishonestLA( $la.2 ) ]->
+   [ State_11112111211( $la.2, lock.2, x2.2, pk.3, $s.4 ) ]
+
+  /*
+  rule (modulo AC) eventDishonestLAla_0_1111211121[color=#408067,
+                                                   process="event DishonestLA( $la.2 );"]:
+     [ State_1111211121( $la, lock, x2, pk, $s ) ]
+    --[ DishonestLA( $la ) ]->
+     [ State_11112111211( $la, lock, x2, pk, $s ) ]
+  */
+
+rule (modulo E) eventTestLAlaspk_0_11112111211[color=#408067,
+                                               process="event TestLA( $la.2, $s.4, pk.3 );"]:
+   [ State_11112111211( $la.2, lock.2, x2.2, pk.3, $s.4 ) ]
+  --[ TestLA( $la.2, $s.4, pk.3 ) ]->
+   [ State_111121112111( $la.2, lock.2, x2.2, pk.3, $s.4 ) ]
+
+  /*
+  rule (modulo AC) eventTestLAlaspk_0_11112111211[color=#408067,
+                                                  process="event TestLA( $la.2, $s.4, pk.3 );"]:
+     [ State_11112111211( $la, lock, x2, pk, $s ) ]
+    --[ TestLA( $la, $s, pk ) ]->
+     [ State_111121112111( $la, lock, x2, pk, $s ) ]
+  */
+
+rule (modulo E) unlocklog_0_111121112111[color=#408067,
+                                         process="unlock 'log';"]:
+   [ State_111121112111( $la.2, lock.2, x2.2, pk.3, $s.4 ) ]
+  --[ Unlock_2( '2', lock.2, 'log' ), Unlock( '2', lock.2, 'log' ) ]->
+   [ ]
+
+  /*
+  rule (modulo AC) unlocklog_0_111121112111[color=#408067,
+                                            process="unlock 'log';"]:
+     [ State_111121112111( $la, lock, x2, pk, $s ) ]
+    --[ Unlock_2( '2', lock, 'log' ), Unlock( '2', lock, 'log' ) ]->
+     [ ]
+  */
+
+rule (modulo E) lookuplalogspksasx_1_111121112[color=#408067,
+                                               process="lookup <$la.2, 'log', $s.4, pk.3, 's1'> as x2.2"]:
+   [ State_111121112( $la.2, lock.2, pk.3, $s.4 ) ]
+  --[ IsNotSet( <$la.2, 'log', $s.4, pk.3, 's1'> ) ]->
+   [ ]
+
+  /*
+  rule (modulo AC) lookuplalogspksasx_1_111121112[color=#408067,
+                                                  process="lookup <$la.2, 'log', $s.4, pk.3, 's1'> as x2.2"]:
+     [ State_111121112( $la, lock, pk, $s ) ]
+    --[ IsNotSet( <$la, 'log', $s, pk, 's1'> ) ]->
+     [ ]
+  */
+
+rule (modulo E) p_1_11[color=#408053, process="!"]:
+   [ !Semistate_111( ) ]
+  -->
+   [
+   State_11121( ), State_111121( ), State_1111121( ), State_1111111( ),
+   State_1111112( )
+   ]
+
+  /* has exactly the trivial AC variant */
+
+rule (modulo E) locktestCA_0_11121[color=#408068,
+                                   process="lock 'testCA';"]:
+   [ State_11121( ), Fr( lock.3 ) ]
+  --[ Lock_3( '3', lock.3, 'testCA' ), Lock( '3', lock.3, 'testCA' ) ]->
+   [ State_111211( lock.3 ) ]
+
+  /*
+  rule (modulo AC) locktestCA_0_11121[color=#408068,
+                                      process="lock 'testCA';"]:
+     [ State_11121( ), Fr( lock ) ]
+    --[ Lock_3( '3', lock, 'testCA' ), Lock( '3', lock, 'testCA' ) ]->
+     [ State_111211( lock ) ]
+  */
+
+rule (modulo E) locklog_0_111211[color=#40807d, process="lock 'log';"]:
+   [ State_111211( lock.3 ), Fr( lock.4 ) ]
+  --[ Lock_4( '4', lock.4, 'log' ), Lock( '4', lock.4, 'log' ) ]->
+   [ State_1112111( lock.3, lock.4 ) ]
+
+  /*
+  rule (modulo AC) locklog_0_111211[color=#40807d, process="lock 'log';"]:
+     [ State_111211( lock ), Fr( lock.1 ) ]
+    --[ Lock_4( '4', lock.1, 'log' ), Lock( '4', lock.1, 'log' ) ]->
+     [ State_1112111( lock, lock.1 ) ]
+  */
+
+rule (modulo E) eventTerminate_0_1112111[color=#40807d,
+                                         process="event Terminate( );"]:
+   [ State_1112111( lock.3, lock.4 ) ] --[ Terminate( ) ]-> [ ]
+
+  /*
+  rule (modulo AC) eventTerminate_0_1112111[color=#40807d,
+                                            process="event Terminate( );"]:
+     [ State_1112111( lock, lock.1 ) ] --[ Terminate( ) ]-> [ ]
+  */
+
+rule (modulo E) Init[color=#ffffff, process="|"]:
+   [ ] --[ Init( ) ]-> [ !Semistate_21( ), !Semistate_111( ) ]
+
+  /* has exactly the trivial AC variant */
+
+rule (modulo E) incCAcorruptca_0_211[color=#ffffff,
+                                     process="in('c',<'CAcorrupt', $ca.5>);"]:
+   [ State_211( ), Message( 'c', x ) ] --> [ Let_2111( x ), Ack( 'c', x ) ]
+
+  /* has exactly the trivial AC variant */
+
+rule (modulo E) incCAcorruptca_2_211[color=#ffffff,
+                                     process="in('c',<'CAcorrupt', $ca.5>);"]:
+   [ State_211( ), In( <'c', x> ) ] --> [ Let_2111( x ) ]
+
+  /* has exactly the trivial AC variant */
+
+rule (modulo E) incCAcorruptca_1_211[color=#ffffff,
+                                     process="in('c',<'CAcorrupt', $ca.5>);"]:
+   [ Let_2111( <'CAcorrupt', $ca.5> ) ] --> [ State_2111( $ca.5 ) ]
+
+  /*
+  rule (modulo AC) incCAcorruptca_1_211[color=#ffffff,
+                                        process="in('c',<'CAcorrupt', $ca.5>);"]:
+     [ Let_2111( <'CAcorrupt', $ca> ) ] --> [ State_2111( $ca ) ]
+  */
+
+rule (modulo E) incCAcorruptca_3_211[color=#ffffff,
+                                     process="in('c',<'CAcorrupt', $ca.5>);"]:
+   [ Let_2111( <'CAcorrupt', $ca.5> ) ] --> [ State_2111( $ca.5 ) ]
+
+  /*
+  rule (modulo AC) incCAcorruptca_3_211[color=#ffffff,
+                                        process="in('c',<'CAcorrupt', $ca.5>);"]:
+     [ Let_2111( <'CAcorrupt', $ca> ) ] --> [ State_2111( $ca ) ]
+  */
+
+rule (modulo E) eventCorruptedca_0_2111[color=#ffffff,
+                                        process="event Corrupted( $ca.5 );"]:
+   [ State_2111( $ca.5 ) ]
+  --[ Corrupted( $ca.5 ) ]->
+   [ State_21111( $ca.5 ) ]
+
+  // loop breaker: [0]
+  /*
+  rule (modulo AC) eventCorruptedca_0_2111[color=#ffffff,
+                                           process="event Corrupted( $ca.5 );"]:
+     [ State_2111( $ca ) ] --[ Corrupted( $ca ) ]-> [ State_21111( $ca ) ]
+    // loop breaker: [0]
+  */
+
+rule (modulo E) outcskcaca_1_21111[color=#ffffff,
+                                   process="out('c',skca($ca.5));"]:
+   [ State_21111( $ca.5 ) ]
+  -->
+   [ Message( 'c', skca($ca.5) ), Semistate_211111( $ca.5 ) ]
+
+  /*
+  rule (modulo AC) outcskcaca_1_21111[color=#ffffff,
+                                      process="out('c',skca($ca.5));"]:
+     [ State_21111( $ca ) ]
+    -->
+     [ Message( 'c', skca($ca) ), Semistate_211111( $ca ) ]
+  */
+
+rule (modulo E) outcskcaca_0_21111[color=#ffffff,
+                                   process="out('c',skca($ca.5));"]:
+   [ State_21111( $ca.5 ), In( 'c' ) ]
+  -->
+   [ Out( skca($ca.5) ), State_211111( $ca.5 ) ]
+
+  /*
+  rule (modulo AC) outcskcaca_0_21111[color=#ffffff,
+                                      process="out('c',skca($ca.5));"]:
+     [ State_21111( $ca ), In( 'c' ) ]
+    -->
+     [ Out( skca($ca) ), State_211111( $ca ) ]
+  */
+
+rule (modulo E) outcskcaca_2_21111[color=#ffffff,
+                                   process="out('c',skca($ca.5));"]:
+   [ Semistate_211111( $ca.5 ), Ack( 'c', skca($ca.5) ) ]
+  -->
+   [ State_211111( $ca.5 ) ]
+
+  /*
+  rule (modulo AC) outcskcaca_2_21111[color=#ffffff,
+                                      process="out('c',skca($ca.5));"]:
+     [ Semistate_211111( $ca ), Ack( 'c', skca($ca) ) ]
+    -->
+     [ State_211111( $ca ) ]
+  */
+
+rule (modulo E) p_1_2[color=#ffffff, process="!"]:
+   [ !Semistate_21( ) ] --> [ !Semistate_2121( ), State_211( ) ]
+
+  /* has exactly the trivial AC variant */
+
+rule (modulo E) p_1_212[color=#ffffff, process="!"]:
+   [ !Semistate_2121( ) ] --> [ State_2121( ) ]
+
+  /* has exactly the trivial AC variant */
+
+rule (modulo E) inclaLAcorruptid_0_2121[color=#ffffff,
+                                        process="in('c',<$la.3, 'LAcorrupt', $id.1>);"]:
+   [ State_2121( ), Message( 'c', x ) ]
+  -->
+   [ Let_21211( x ), Ack( 'c', x ) ]
+
+  /* has exactly the trivial AC variant */
+
+rule (modulo E) inclaLAcorruptid_2_2121[color=#ffffff,
+                                        process="in('c',<$la.3, 'LAcorrupt', $id.1>);"]:
+   [ State_2121( ), In( <'c', x> ) ] --> [ Let_21211( x ) ]
+
+  /* has exactly the trivial AC variant */
+
+rule (modulo E) inclaLAcorruptid_1_2121[color=#ffffff,
+                                        process="in('c',<$la.3, 'LAcorrupt', $id.1>);"]:
+   [ Let_21211( <$la.3, 'LAcorrupt', $id.1> ) ]
+  -->
+   [ State_21211( $id.1, $la.3 ) ]
+
+  /*
+  rule (modulo AC) inclaLAcorruptid_1_2121[color=#ffffff,
+                                           process="in('c',<$la.3, 'LAcorrupt', $id.1>);"]:
+     [ Let_21211( <$la, 'LAcorrupt', $id> ) ] --> [ State_21211( $id, $la ) ]
+  */
+
+rule (modulo E) inclaLAcorruptid_3_2121[color=#ffffff,
+                                        process="in('c',<$la.3, 'LAcorrupt', $id.1>);"]:
+   [ Let_21211( <$la.3, 'LAcorrupt', $id.1> ) ]
+  -->
+   [ State_21211( $id.1, $la.3 ) ]
+
+  /*
+  rule (modulo AC) inclaLAcorruptid_3_2121[color=#ffffff,
+                                           process="in('c',<$la.3, 'LAcorrupt', $id.1>);"]:
+     [ Let_21211( <$la, 'LAcorrupt', $id> ) ] --> [ State_21211( $id, $la ) ]
+  */
+
+rule (modulo E) eventCorruptedla_0_21211[color=#ffffff,
+                                         process="event Corrupted( $la.3 );"]:
+   [ State_21211( $id.1, $la.3 ) ]
+  --[ Corrupted( $la.3 ) ]->
+   [ !Semistate_2121111( $id.1, $la.3 ) ]
+
+  /*
+  rule (modulo AC) eventCorruptedla_0_21211[color=#ffffff,
+                                            process="event Corrupted( $la.3 );"]:
+     [ State_21211( $id, $la ) ]
+    --[ Corrupted( $la ) ]->
+     [ !Semistate_2121111( $id, $la ) ]
+  */
+
+rule (modulo E) p_1_212111[color=#ffffff, process="!"]:
+   [ !Semistate_2121111( $id.1, $la.3 ) ]
+  -->
+   [ State_2121111( $id.1, $la.3 ) ]
+
+  /*
+  rule (modulo AC) p_1_212111[color=#ffffff, process="!"]:
+     [ !Semistate_2121111( $id, $la ) ] --> [ State_2121111( $id, $la ) ]
+  */
+
+rule (modulo E) incSpkentity_0_2121111[color=#ffffff,
+                                       process="in('c',<S.1, pk.4, entity.1>);"]:
+   [ State_2121111( $id.1, $la.3 ), Message( 'c', x.4 ) ]
+  -->
+   [ Let_21211111( x.4, $id.1, $la.3 ), Ack( 'c', x.4 ) ]
+
+  /*
+  rule (modulo AC) incSpkentity_0_2121111[color=#ffffff,
+                                          process="in('c',<S.1, pk.4, entity.1>);"]:
+     [ State_2121111( $id, $la ), Message( 'c', x ) ]
+    -->
+     [ Let_21211111( x, $id, $la ), Ack( 'c', x ) ]
+  */
+
+rule (modulo E) incSpkentity_2_2121111[color=#ffffff,
+                                       process="in('c',<S.1, pk.4, entity.1>);"]:
+   [ State_2121111( $id.1, $la.3 ), In( <'c', x.4> ) ]
+  -->
+   [ Let_21211111( x.4, $id.1, $la.3 ) ]
+
+  /*
+  rule (modulo AC) incSpkentity_2_2121111[color=#ffffff,
+                                          process="in('c',<S.1, pk.4, entity.1>);"]:
+     [ State_2121111( $id, $la ), In( <'c', x> ) ]
+    -->
+     [ Let_21211111( x, $id, $la ) ]
+  */
+
+rule (modulo E) incSpkentity_1_2121111[color=#ffffff,
+                                       process="in('c',<S.1, pk.4, entity.1>);"]:
+   [ Let_21211111( <S.1, pk.4, entity.1>, $id.1, $la.3 ) ]
+  -->
+   [ State_21211111( $id.1, S.1, entity.1, $la.3, pk.4 ) ]
+
+  /*
+  rule (modulo AC) incSpkentity_1_2121111[color=#ffffff,
+                                          process="in('c',<S.1, pk.4, entity.1>);"]:
+     [ Let_21211111( <S, pk, entity>, $id, $la ) ]
+    -->
+     [ State_21211111( $id, S, entity, $la, pk ) ]
+  */
+
+rule (modulo E) incSpkentity_3_2121111[color=#ffffff,
+                                       process="in('c',<S.1, pk.4, entity.1>);"]:
+   [ Let_21211111( <S.1, pk.4, entity.1>, $id.1, $la.3 ) ]
+  -->
+   [ State_21211111( $id.1, S.1, entity.1, $la.3, pk.4 ) ]
+
+  /*
+  rule (modulo AC) incSpkentity_3_2121111[color=#ffffff,
+                                          process="in('c',<S.1, pk.4, entity.1>);"]:
+     [ Let_21211111( <S, pk, entity>, $id, $la ) ]
+    -->
+     [ State_21211111( $id, S, entity, $la, pk ) ]
+  */
+
+rule (modulo E) locklog_0_21211111[color=#ffffff, process="lock 'log';"]:
+   [ State_21211111( $id.1, S.1, entity.1, $la.3, pk.4 ), Fr( lock.5 ) ]
+  --[ Lock_5( '5', lock.5, 'log' ), Lock( '5', lock.5, 'log' ) ]->
+   [ State_212111111( $id.1, S.1, entity.1, $la.3, pk.4, lock.5 ) ]
+
+  /*
+  rule (modulo AC) locklog_0_21211111[color=#ffffff,
+                                      process="lock 'log';"]:
+     [ State_21211111( $id, S, entity, $la, pk ), Fr( lock ) ]
+    --[ Lock_5( '5', lock, 'log' ), Lock( '5', lock, 'log' ) ]->
+     [ State_212111111( $id, S, entity, $la, pk, lock ) ]
+  */
+
+rule (modulo E) insertlalogSpkentityyes_0_212111111[color=#ffffff,
+                                                    process="insert <$la.3, 'log', S.1, pk.4, entity.1>,'yes';"]:
+   [ State_212111111( $id.1, S.1, entity.1, $la.3, pk.4, lock.5 ) ]
+  --[ Insert( <$la.3, 'log', S.1, pk.4, entity.1>, 'yes' ) ]->
+   [ State_2121111111( $id.1, S.1, entity.1, $la.3, pk.4, lock.5 ) ]
+
+  /*
+  rule (modulo AC) insertlalogSpkentityyes_0_212111111[color=#ffffff,
+                                                       process="insert <$la.3, 'log', S.1, pk.4, entity.1>,'yes';"]:
+     [ State_212111111( $id, S, entity, $la, pk, lock ) ]
+    --[ Insert( <$la, 'log', S, pk, entity>, 'yes' ) ]->
+     [ State_2121111111( $id, S, entity, $la, pk, lock ) ]
+  */
+
+rule (modulo E) unlocklog_0_2121111111[color=#ffffff,
+                                       process="unlock 'log';"]:
+   [ State_2121111111( $id.1, S.1, entity.1, $la.3, pk.4, lock.5 ) ]
+  --[ Unlock_5( '5', lock.5, 'log' ), Unlock( '5', lock.5, 'log' ) ]->
+   [ ]
+
+  /*
+  rule (modulo AC) unlocklog_0_2121111111[color=#ffffff,
+                                          process="unlock 'log';"]:
+     [ State_2121111111( $id, S, entity, $la, pk, lock ) ]
+    --[ Unlock_5( '5', lock, 'log' ), Unlock( '5', lock, 'log' ) ]->
+     [ ]
+  */
+
+restriction set_in:
+  "∀ x y #t3.
+    (IsIn( x, y ) @ #t3) ⇒
+    (∃ #t2.
+      ((Insert( x, y ) @ #t2) ∧ (#t2 < #t3)) ∧
+      (∀ #t1 yp.
+        (Insert( x, yp ) @ #t1) ⇒ (((#t1 < #t2) ∨ (#t1 = #t2)) ∨ (#t3 < #t1))))"
+
+restriction set_notin:
+  "∀ x #t3.
+    (IsNotSet( x ) @ #t3) ⇒ (∀ #t1 y. (Insert( x, y ) @ #t1) ⇒ (#t3 < #t1))"
+  // safety formula
+
+restriction single_session:
+  "∀ #i #j. ((Init( ) @ #i) ∧ (Init( ) @ #j)) ⇒ (#i = #j)"
+  // safety formula
+
+restriction locking_0:
+  "∀ p pp l x lp #t1 #t3.
+    ((Lock_0( p, l, x ) @ #t1) ∧ (Lock( pp, lp, x ) @ #t3)) ⇒
+    ((((#t1 < #t3) ∧
+       (∃ #t2.
+         (((((Unlock_0( p, l, x ) @ #t2) ∧ (#t1 < #t2)) ∧ (#t2 < #t3)) ∧
+           (∀ #t0 pp.1. (Unlock( pp.1, l, x ) @ #t0) ⇒ (#t0 = #t2))) ∧
+          (∀ pp.1 lpp #t0.
+            (Lock( pp.1, lpp, x ) @ #t0) ⇒
+            (((#t0 < #t1) ∨ (#t0 = #t1)) ∨ (#t2 < #t0)))) ∧
+         (∀ pp.1 lpp #t0.
+           (Unlock( pp.1, lpp, x ) @ #t0) ⇒
+           (((#t0 < #t1) ∨ (#t2 < #t0)) ∨ (#t2 = #t0))))) ∨
+      (#t3 < #t1)) ∨
+     (#t1 = #t3))"
+
+restriction locking_1:
+  "∀ p pp l x lp #t1 #t3.
+    ((Lock_1( p, l, x ) @ #t1) ∧ (Lock( pp, lp, x ) @ #t3)) ⇒
+    ((((#t1 < #t3) ∧
+       (∃ #t2.
+         (((((Unlock_1( p, l, x ) @ #t2) ∧ (#t1 < #t2)) ∧ (#t2 < #t3)) ∧
+           (∀ #t0 pp.1. (Unlock( pp.1, l, x ) @ #t0) ⇒ (#t0 = #t2))) ∧
+          (∀ pp.1 lpp #t0.
+            (Lock( pp.1, lpp, x ) @ #t0) ⇒
+            (((#t0 < #t1) ∨ (#t0 = #t1)) ∨ (#t2 < #t0)))) ∧
+         (∀ pp.1 lpp #t0.
+           (Unlock( pp.1, lpp, x ) @ #t0) ⇒
+           (((#t0 < #t1) ∨ (#t2 < #t0)) ∨ (#t2 = #t0))))) ∨
+      (#t3 < #t1)) ∨
+     (#t1 = #t3))"
+
+restriction locking_2:
+  "∀ p pp l x lp #t1 #t3.
+    ((Lock_2( p, l, x ) @ #t1) ∧ (Lock( pp, lp, x ) @ #t3)) ⇒
+    ((((#t1 < #t3) ∧
+       (∃ #t2.
+         (((((Unlock_2( p, l, x ) @ #t2) ∧ (#t1 < #t2)) ∧ (#t2 < #t3)) ∧
+           (∀ #t0 pp.1. (Unlock( pp.1, l, x ) @ #t0) ⇒ (#t0 = #t2))) ∧
+          (∀ pp.1 lpp #t0.
+            (Lock( pp.1, lpp, x ) @ #t0) ⇒
+            (((#t0 < #t1) ∨ (#t0 = #t1)) ∨ (#t2 < #t0)))) ∧
+         (∀ pp.1 lpp #t0.
+           (Unlock( pp.1, lpp, x ) @ #t0) ⇒
+           (((#t0 < #t1) ∨ (#t2 < #t0)) ∨ (#t2 = #t0))))) ∨
+      (#t3 < #t1)) ∨
+     (#t1 = #t3))"
+
+restriction locking_5:
+  "∀ p pp l x lp #t1 #t3.
+    ((Lock_5( p, l, x ) @ #t1) ∧ (Lock( pp, lp, x ) @ #t3)) ⇒
+    ((((#t1 < #t3) ∧
+       (∃ #t2.
+         (((((Unlock_5( p, l, x ) @ #t2) ∧ (#t1 < #t2)) ∧ (#t2 < #t3)) ∧
+           (∀ #t0 pp.1. (Unlock( pp.1, l, x ) @ #t0) ⇒ (#t0 = #t2))) ∧
+          (∀ pp.1 lpp #t0.
+            (Lock( pp.1, lpp, x ) @ #t0) ⇒
+            (((#t0 < #t1) ∨ (#t0 = #t1)) ∨ (#t2 < #t0)))) ∧
+         (∀ pp.1 lpp #t0.
+           (Unlock( pp.1, lpp, x ) @ #t0) ⇒
+           (((#t0 < #t1) ∨ (#t2 < #t0)) ∨ (#t2 = #t0))))) ∨
+      (#t3 < #t1)) ∨
+     (#t1 = #t3))"
+
+restriction locking_3:
+  "∀ p pp l x lp #t1 #t3.
+    ((Lock_3( p, l, x ) @ #t1) ∧ (Lock( pp, lp, x ) @ #t3)) ⇒
+    ((#t3 < #t1) ∨ (#t1 = #t3))"
+  // safety formula
+
+restriction locking_4:
+  "∀ p pp l x lp #t1 #t3.
+    ((Lock_4( p, l, x ) @ #t1) ∧ (Lock( pp, lp, x ) @ #t3)) ⇒
+    ((#t3 < #t1) ∨ (#t1 = #t3))"
+  // safety formula
+
+lemma accCA_tCA_suff:
+  exists-trace
+  "∃ ca #i.
+    ((DishonestCA( ca ) @ #i) ∧
+     (∀ ca.1 #i.1. (DishonestCA( ca.1 ) @ #i.1) ⇒ (ca.1 = ca))) ∧
+    (∀ a #i.1. (Corrupted( a ) @ #i.1) ⇒ (a = ca))"
+/*
+guarded formula characterizing all satisfying traces:
+"∃ ca #i.
+  (DishonestCA( ca ) @ #i)
+ ∧
+  (∀ ca.1 #i.1. (DishonestCA( ca.1 ) @ #i.1) ⇒ ca.1 = ca) ∧
+  (∀ a #i.1. (Corrupted( a ) @ #i.1) ⇒ a = ca)"
+*/
+simplify
+solve( State_1111121112( lock, pk, $s, $ca ) ▶₀ #i )
+  case lookupcaproofOfIDspkasignored_1_111112111
+  solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+    case locklog_0_111211
+    solve( Unlock_1( '1', ~n, 'testCA' ) @ #t2 )
+      case unlocktestCA_0_111112111211
+      solve( State_111112111211( ~n, pk.1, $s.1, $ca.1 ) ▶₀ #t2 )
+        case eventTestCAcaspk_0_11111211121
+        solve( !KU( sign(skca($ca), <pk, $s>) ) @ #vk )
+          case c_sign
+          solve( !KU( skca($ca) ) @ #vk.1 )
+            case outcskcaca_0_21111
+            solve( State_2111( $ca ) ▶₀ #vr.9 )
+              case incCAcorruptca_1_211
+              SOLVED // trace found
+            qed
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma accCA_verif_empty:
+  all-traces
+  "(¬(∃ ca #i. DishonestCA( ca ) @ #i)) ⇒
+   (∀ ca s pk #i.
+     (TestCA( ca, s, pk ) @ #i) ⇒ (∃ #j. HonestRegister( s, ca, pk ) @ #j))"
+/*
+guarded formula characterizing all counter-examples:
+"(∀ ca #i. (DishonestCA( ca ) @ #i) ⇒ ⊥) ∧
+ (∃ ca s pk #i.
+   (TestCA( ca, s, pk ) @ #i)
+  ∧
+   ∀ #j. (HonestRegister( s, ca, pk ) @ #j) ⇒ ⊥)"
+*/
+simplify
+solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+  case locklog_0_111211
+  solve( TestCA( ca, s, pk ) @ #i )
+    case eventTestCAcaspk_0_11111211111
+    solve( State_11111211111( ignored, lock, pk, $s, $ca ) ▶₀ #i )
+      case eventHonestCAca_0_1111121111
+      solve( Unlock_1( '1', ~n, 'testCA' ) @ #t2 )
+        case unlocktestCA_0_111112111111
+        solve( State_111112111111( ignored.1, ~n, pk.1, $s.1, $ca.1 ) ▶₀ #t2 )
+          case eventTestCAcaspk_0_11111211111
+          solve( (#t2.1 < #t2.2)  ∥ (#t2.1 = #t2.2) )
+            case case_1
+            by contradiction /* from formulas */
+          next
+            case case_2
+            solve( !KU( sign(skca($ca), <pk, $s>) ) @ #vk )
+              case c_sign
+              solve( !KU( skca($ca) ) @ #vk.1 )
+                case outcskcaca_0_21111
+                solve( State_2111( $ca ) ▶₀ #vr.9 )
+                  case incCAcorruptca_1_211
+                  solve( Insert( <$ca, 'proofOfID', $s, pk>, ignored ) @ #t2.1 )
+                    case insertcaproofOfIDspkskSyes_0_11111111111111
+                    solve( State_11111111111111( $ca.1, $s, skS, $ca ) ▶₀ #t2.1 )
+                      case p_1_1111111111
+                      by contradiction /* from formulas */
+                    qed
+                  qed
+                next
+                  case incCAcorruptca_3_211
+                  solve( Insert( <$ca, 'proofOfID', $s, pk>, ignored ) @ #t2.1 )
+                    case insertcaproofOfIDspkskSyes_0_11111111111111
+                    solve( State_11111111111111( $ca.1, $s, skS, $ca ) ▶₀ #t2.1 )
+                      case p_1_1111111111
+                      by contradiction /* from formulas */
+                    qed
+                  qed
+                qed
+              qed
+            next
+              case outsignskcacapkskSs_0_1111111111111111
+              by contradiction /* from formulas */
+            qed
+          qed
+        qed
+      next
+        case unlocktestCA_0_111112111211
+        by solve( State_111112111211( ~n, pk.1, $s.1, $ca.1 ) ▶₀ #t2 )
+      qed
+    qed
+  next
+    case eventTestCAcaspk_0_11111211121
+    solve( State_11111211121( lock, pk, $s, $ca ) ▶₀ #i )
+      case eventDishonestCAca_0_1111121112
+      by contradiction /* from formulas */
+    qed
+  qed
+qed
+
+lemma accCA_tCA_verif_nonempty:
+  all-traces
+  "∀ ca #i.
+    (DishonestCA( ca ) @ #i) ⇒
+    (¬(∀ ca.1 s pk #i.1.
+        (TestCA( ca.1, s, pk ) @ #i.1) ⇒
+        (∃ #j. HonestRegister( s, ca.1, pk ) @ #j)))"
+/*
+guarded formula characterizing all counter-examples:
+"∃ ca #i.
+  (DishonestCA( ca ) @ #i)
+ ∧
+  ∀ ca.1 s pk #i.1.
+   (TestCA( ca.1, s, pk ) @ #i.1)
+  ⇒
+   ∃ #j. (HonestRegister( s, ca.1, pk ) @ #j)"
+*/
+simplify
+solve( State_1111121112( lock, pk, $s, $ca ) ▶₀ #i )
+  case lookupcaproofOfIDspkasignored_1_111112111
+  solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+    case locklog_0_111211
+    solve( Unlock_1( '1', ~n, 'testCA' ) @ #t2 )
+      case unlocktestCA_0_111112111111
+      by solve( State_111112111111( ignored, ~n, pk.1, $s.1, $ca.1 ) ▶₀ #t2 )
+    next
+      case unlocktestCA_0_111112111211
+      solve( State_111112111211( ~n, pk.1, $s.1, $ca.1 ) ▶₀ #t2 )
+        case eventTestCAcaspk_0_11111211121
+        solve( !Semistate_11111111111( $ca.1 ) ▶₀ #j )
+          case inca_0_1111111
+          solve( !KU( sign(skca($ca), <pk(~n.1), $s>) ) @ #vk )
+            case c_sign
+            solve( !KU( skca($ca) ) @ #vk.6 )
+              case outcskcaca_0_21111
+              solve( State_2111( $ca ) ▶₀ #vr.11 )
+                case incCAcorruptca_1_211
+                solve( !KU( pk(~n.1) ) @ #vk.8 )
+                  case c_pk
+                  by solve( !KU( ~n.1 ) @ #vk.12 )
+                next
+                  case insertcaproofOfIDspkskSyes_0_11111111111111
+                  by contradiction /* cyclic */
+                next
+                  case outsignskcacapkskSs_0_1111111111111111
+                  by contradiction /* cyclic */
+                qed
+              next
+                case incCAcorruptca_3_211
+                solve( !KU( pk(~n.1) ) @ #vk.8 )
+                  case c_pk
+                  by solve( !KU( ~n.1 ) @ #vk.12 )
+                next
+                  case insertcaproofOfIDspkskSyes_0_11111111111111
+                  by contradiction /* cyclic */
+                next
+                  case outsignskcacapkskSs_0_1111111111111111
+                  by contradiction /* cyclic */
+                qed
+              qed
+            qed
+          next
+            case outsignskcacapkskSs_0_1111111111111111
+            by contradiction /* cyclic */
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma accCA_tCA_min:
+  all-traces
+  "∀ ca #i.
+    (DishonestCA( ca ) @ #i) ⇒
+    (¬(∃ ca.1 #i.1.
+        (DishonestCA( ca.1 ) @ #i.1) ∧ ((ca.1 = ca) ∧ (¬(ca = ca.1)))))"
+/*
+guarded formula characterizing all counter-examples:
+"∃ ca #i.
+  (DishonestCA( ca ) @ #i)
+ ∧
+  ∃ ca.1 #i.1. (DishonestCA( ca.1 ) @ #i.1) ∧ (ca.1 = ca) ∧ ¬(ca = ca.1)"
+*/
+simplify
+by contradiction /* from formulas */
+
+lemma accCA_tCA_uniq:
+  all-traces
+  "∀ ca #i. (DishonestCA( ca ) @ #i) ⇒ (∃ #i.1. Corrupted( ca ) @ #i.1)"
+/*
+guarded formula characterizing all counter-examples:
+"∃ ca #i.
+  (DishonestCA( ca ) @ #i) ∧ ∀ #i.1. (Corrupted( ca ) @ #i.1) ⇒ ⊥"
+*/
+simplify
+solve( State_1111121112( lock, pk, $s, $ca ) ▶₀ #i )
+  case lookupcaproofOfIDspkasignored_1_111112111
+  solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+    case locklog_0_111211
+    solve( Unlock_1( '1', ~n, 'testCA' ) @ #t2 )
+      case unlocktestCA_0_111112111111
+      by solve( State_111112111111( ignored, ~n, pk.1, $s.1, $ca.1 ) ▶₀ #t2 )
+    next
+      case unlocktestCA_0_111112111211
+      solve( State_111112111211( ~n, pk.1, $s.1, $ca.1 ) ▶₀ #t2 )
+        case eventTestCAcaspk_0_11111211121
+        solve( !KU( sign(skca($ca), <pk, $s>) ) @ #vk )
+          case c_sign
+          solve( !KU( skca($ca) ) @ #vk.1 )
+            case outcskcaca_0_21111
+            by contradiction /* from formulas */
+          qed
+        next
+          case outsignskcacapkskSs_0_1111111111111111
+          by contradiction /* cyclic */
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma accCA_tCA_inj:
+  all-traces "⊤"
+/*
+guarded formula characterizing all counter-examples:
+"⊥"
+*/
+by contradiction /* from formulas */
+
+lemma accCA_tCA_single:
+  exists-trace
+  "∃ ca #i.
+    (DishonestCA( ca ) @ #i) ∧
+    (∀ ca.1 #i.1. (DishonestCA( ca.1 ) @ #i.1) ⇒ (ca.1 = ca))"
+/*
+guarded formula characterizing all satisfying traces:
+"∃ ca #i.
+  (DishonestCA( ca ) @ #i)
+ ∧
+  ∀ ca.1 #i.1. (DishonestCA( ca.1 ) @ #i.1) ⇒ ca.1 = ca"
+*/
+simplify
+solve( State_1111121112( lock, pk, $s, $ca ) ▶₀ #i )
+  case lookupcaproofOfIDspkasignored_1_111112111
+  solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+    case locklog_0_111211
+    solve( Unlock_1( '1', ~n, 'testCA' ) @ #t2 )
+      case unlocktestCA_0_111112111211
+      solve( State_111112111211( ~n, pk.1, $s.1, $ca.1 ) ▶₀ #t2 )
+        case eventTestCAcaspk_0_11111211121
+        solve( !KU( sign(skca($ca), <pk, $s>) ) @ #vk )
+          case c_sign
+          solve( !KU( skca($ca) ) @ #vk.1 )
+            case outcskcaca_0_21111
+            solve( State_2111( $ca ) ▶₀ #vr.9 )
+              case incCAcorruptca_1_211
+              SOLVED // trace found
+            qed
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma accLA_tLA_suff:
+  exists-trace
+  "∃ la #i.
+    ((DishonestLA( la ) @ #i) ∧
+     (∀ la.1 #i.1. (DishonestLA( la.1 ) @ #i.1) ⇒ (la.1 = la))) ∧
+    (∀ a #i.1. (Corrupted( a ) @ #i.1) ⇒ (a = la))"
+/*
+guarded formula characterizing all satisfying traces:
+"∃ la #i.
+  (DishonestLA( la ) @ #i)
+ ∧
+  (∀ la.1 #i.1. (DishonestLA( la.1 ) @ #i.1) ⇒ la.1 = la) ∧
+  (∀ a #i.1. (Corrupted( a ) @ #i.1) ⇒ a = la)"
+*/
+simplify
+solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+  case locklog_0_111211
+  solve( DishonestLA( la ) @ #i )
+    case eventDishonestLAla_0_1111211112
+    solve( State_1111211112( x1, $la, lock, pk, $s ) ▶₀ #i )
+      case lookuplalogspksasx_1_111121111
+      solve( Unlock_2( '2', ~n, 'log' ) @ #t2 )
+        case unlocklog_0_111121111211
+        solve( State_111121111211( x1.1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+          case eventTestLAlaspk_0_11112111121
+          solve( (#t2.1 < #t2.2)  ∥ (#t2.1 = #t2.2) )
+            case case_2
+            solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #t2.1 )
+              case insertlalogSpkentityyes_0_212111111
+              solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #t2.1 )
+                case locklog_0_21211111_case_1
+                solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                  case insertlalogSpkentityyes_0_212111111
+                  SOLVED // trace found
+                qed
+              qed
+            qed
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma accLA_verif_empty:
+  all-traces
+  "(¬(∃ la #i. DishonestLA( la ) @ #i)) ⇒
+   (∀ la s pk #i.
+     (TestLA( la, s, pk ) @ #i) ⇒
+     ((∃ #j. (Insert( <la, 'log', s, pk, 'c1'>, 'yes' ) @ #j) ∧ (#j < #i)) ∧
+      (∃ #j. (Insert( <la, 'log', s, pk, 's1'>, 'yes' ) @ #j) ∧ (#j < #i))))"
+/*
+guarded formula characterizing all counter-examples:
+"(∀ la #i. (DishonestLA( la ) @ #i) ⇒ ⊥) ∧
+ (∃ la s pk #i.
+   (TestLA( la, s, pk ) @ #i)
+  ∧
+   ((∀ #j. (Insert( <la, 'log', s, pk, 'c1'>, 'yes' ) @ #j) ⇒ ¬(#j < #i)) ∨
+    (∀ #j. (Insert( <la, 'log', s, pk, 's1'>, 'yes' ) @ #j) ⇒ ¬(#j < #i))))"
+*/
+simplify
+solve( (∀ #j.
+         (Insert( <la, 'log', s, pk, 'c1'>, 'yes' ) @ #j) ⇒ ¬(#j < #i))  ∥
+       (∀ #j. (Insert( <la, 'log', s, pk, 's1'>, 'yes' ) @ #j) ⇒ ¬(#j < #i)) )
+  case case_1
+  solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+    case locklog_0_111211
+    solve( TestLA( la, s, pk ) @ #i )
+      case eventTestLAlaspk_0_11112111111
+      solve( State_11112111111( x1, x2, $la, lock, pk, $s ) ▶₀ #i )
+        case eventHonestLA_0_1111211111
+        solve( Unlock_2( '2', ~n, 'log' ) @ #t2 )
+          case unlocklog_0_111121111111
+          solve( State_111121111111( x1.1, x2.1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+            case eventTestLAlaspk_0_11112111111
+            solve( (#t2.2 < #t2.4)  ∥ (#t2.2 = #t2.4) )
+              case case_1
+              by contradiction /* from formulas */
+            next
+              case case_2
+              solve( (#t2.1 < #t2.3)  ∥ (#t2.1 = #t2.3) )
+                case case_1
+                by contradiction /* from formulas */
+              next
+                case case_2
+                solve( Insert( <$la, 'log', $s, pk, 's1'>, x2 ) @ #t2.1 )
+                  case insertlalogSpkentityyes_0_212111111
+                  solve( State_212111111( $id, $s, 's1', $la, pk, lock ) ▶₀ #t2.1 )
+                    case locklog_0_21211111_case_1
+                    solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #t2.3 )
+                        case insertlalogSpkentityyes_0_212111111
+                        by contradiction /* from formulas */
+                      next
+                        case insertlalogspkcyes_0_111111211111
+                        by contradiction /* from formulas */
+                      qed
+                    qed
+                  next
+                    case locklog_0_21211111_case_2
+                    solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #t2.3 )
+                        case insertlalogSpkentityyes_0_212111111
+                        by contradiction /* from formulas */
+                      next
+                        case insertlalogspkcyes_0_111111211111
+                        by contradiction /* from formulas */
+                      qed
+                    qed
+                  next
+                    case locklog_0_21211111_case_3
+                    solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #t2.3 )
+                        case insertlalogSpkentityyes_0_212111111
+                        by contradiction /* from formulas */
+                      next
+                        case insertlalogspkcyes_0_111111211111
+                        by contradiction /* from formulas */
+                      qed
+                    qed
+                  next
+                    case locklog_0_21211111_case_4
+                    solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #t2.3 )
+                        case insertlalogSpkentityyes_0_212111111
+                        by contradiction /* from formulas */
+                      next
+                        case insertlalogspkcyes_0_111111211111
+                        by contradiction /* from formulas */
+                      qed
+                    qed
+                  qed
+                next
+                  case insertlalogspksyes_0_1111112111111
+                  solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #t2.1 )
+                    case insertlalogspkcyes_0_111111211111
+                    by contradiction /* from formulas */
+                  qed
+                qed
+              qed
+            qed
+          qed
+        next
+          case unlocklog_0_111121111211
+          by solve( State_111121111211( x1.1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+        next
+          case unlocklog_0_111121112111
+          by solve( State_111121112111( $la.1, ~n, x2.1, pk.1, $s.1 ) ▶₀ #t2 )
+        qed
+      qed
+    next
+      case eventTestLAlaspk_0_11112111121
+      solve( State_11112111121( x1, $la, lock, pk, $s ) ▶₀ #i )
+        case eventDishonestLAla_0_1111211112
+        by contradiction /* from formulas */
+      qed
+    next
+      case eventTestLAlaspk_0_11112111211
+      solve( State_11112111211( $la, lock, x2, pk, $s ) ▶₀ #i )
+        case eventDishonestLAla_0_1111211121
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case case_2
+  solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+    case locklog_0_111211
+    solve( TestLA( la, s, pk ) @ #i )
+      case eventTestLAlaspk_0_11112111111
+      solve( State_11112111111( x1, x2, $la, lock, pk, $s ) ▶₀ #i )
+        case eventHonestLA_0_1111211111
+        solve( Unlock_2( '2', ~n, 'log' ) @ #t2 )
+          case unlocklog_0_111121111111
+          solve( State_111121111111( x1.1, x2.1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+            case eventTestLAlaspk_0_11112111111
+            solve( (#t2.2 < #t2.4)  ∥ (#t2.2 = #t2.4) )
+              case case_1
+              by contradiction /* from formulas */
+            next
+              case case_2
+              solve( (#t2.1 < #t2.3)  ∥ (#t2.1 = #t2.3) )
+                case case_1
+                by contradiction /* from formulas */
+              next
+                case case_2
+                solve( Insert( <$la, 'log', $s, pk, 's1'>, x2 ) @ #t2.1 )
+                  case insertlalogSpkentityyes_0_212111111
+                  by contradiction /* from formulas */
+                next
+                  case insertlalogspksyes_0_1111112111111
+                  by contradiction /* from formulas */
+                qed
+              qed
+            qed
+          qed
+        next
+          case unlocklog_0_111121111211
+          by solve( State_111121111211( x1.1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+        next
+          case unlocklog_0_111121112111
+          by solve( State_111121112111( $la.1, ~n, x2.1, pk.1, $s.1 ) ▶₀ #t2 )
+        qed
+      qed
+    next
+      case eventTestLAlaspk_0_11112111121
+      solve( State_11112111121( x1, $la, lock, pk, $s ) ▶₀ #i )
+        case eventDishonestLAla_0_1111211112
+        by contradiction /* from formulas */
+      qed
+    next
+      case eventTestLAlaspk_0_11112111211
+      solve( State_11112111211( $la, lock, x2, pk, $s ) ▶₀ #i )
+        case eventDishonestLAla_0_1111211121
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+qed
+
+lemma accLA_tLA_verif_nonempty:
+  all-traces
+  "∀ la #i.
+    (DishonestLA( la ) @ #i) ⇒
+    (¬(∀ la.1 s pk #i.1.
+        (TestLA( la.1, s, pk ) @ #i.1) ⇒
+        ((∃ #j.
+           (Insert( <la.1, 'log', s, pk, 'c1'>, 'yes' ) @ #j) ∧ (#j < #i.1)) ∧
+         (∃ #j.
+           (Insert( <la.1, 'log', s, pk, 's1'>, 'yes' ) @ #j) ∧ (#j < #i.1)))))"
+/*
+guarded formula characterizing all counter-examples:
+"∃ la #i.
+  (DishonestLA( la ) @ #i)
+ ∧
+  ∀ la.1 s pk #i.1.
+   (TestLA( la.1, s, pk ) @ #i.1)
+  ⇒
+   (∃ #j. (Insert( <la.1, 'log', s, pk, 'c1'>, 'yes' ) @ #j) ∧ #j < #i.1) ∧
+   (∃ #j. (Insert( <la.1, 'log', s, pk, 's1'>, 'yes' ) @ #j) ∧ #j < #i.1)"
+*/
+simplify
+solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+  case locklog_0_111211
+  solve( DishonestLA( la ) @ #i )
+    case eventDishonestLAla_0_1111211112
+    solve( State_1111211112( x1, $la, lock, pk, $s ) ▶₀ #i )
+      case lookuplalogspksasx_1_111121111
+      solve( Unlock_2( '2', ~n, 'log' ) @ #t2 )
+        case unlocklog_0_111121111111
+        by solve( State_111121111111( x1.1, x2, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+      next
+        case unlocklog_0_111121111211
+        solve( State_111121111211( x1.1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+          case eventTestLAlaspk_0_11112111121
+          solve( (#j.1 < #t2.2)  ∥ (#j.1 = #t2.2)  ∥ (#vr.5 < #j.1) )
+            case case_1
+            solve( (#t2.2 < #t2.1)  ∥ (#t2.2 = #t2.1) )
+              case case_1
+              by contradiction /* from formulas */
+            next
+              case case_2
+              solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #t2.1 )
+                case insertlalogSpkentityyes_0_212111111
+                solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #t2.1 )
+                  case locklog_0_21211111_case_1
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j.1 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        next
+                          case case_3
+                          by contradiction /* cyclic */
+                        qed
+                      next
+                        case locklog_0_21211111_case_2
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      next
+                        case locklog_0_21211111_case_3
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      next
+                        case locklog_0_21211111_case_4
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        solve( State_111111211111111( ~n.1, $la.1, pk.1, $s.1, $ca.1 ) ▶₀ #t2.3 )
+                          case insertlalogspkiyes_0_11111121111111
+                          by contradiction /* cyclic */
+                        qed
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_2
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j.1 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      next
+                        case locklog_0_21211111_case_2
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        next
+                          case case_3
+                          by contradiction /* cyclic */
+                        qed
+                      next
+                        case locklog_0_21211111_case_3
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      next
+                        case locklog_0_21211111_case_4
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        solve( State_111111211111111( ~n.1, $la.1, pk.1, $s.1, $ca.1 ) ▶₀ #t2.3 )
+                          case insertlalogspkiyes_0_11111121111111
+                          by contradiction /* cyclic */
+                        qed
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_3
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j.1 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      next
+                        case locklog_0_21211111_case_2
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      next
+                        case locklog_0_21211111_case_3
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        next
+                          case case_3
+                          by contradiction /* cyclic */
+                        qed
+                      next
+                        case locklog_0_21211111_case_4
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        solve( State_111111211111111( ~n.1, $la.1, pk.1, $s.1, $ca.1 ) ▶₀ #t2.3 )
+                          case insertlalogspkiyes_0_11111121111111
+                          by contradiction /* cyclic */
+                        qed
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_4
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j.1 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      next
+                        case locklog_0_21211111_case_2
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      next
+                        case locklog_0_21211111_case_3
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      next
+                        case locklog_0_21211111_case_4
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        next
+                          case case_3
+                          by contradiction /* cyclic */
+                        qed
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        solve( State_111111211111111( ~n.1, $la.1, pk.1, $s.1, $ca.1 ) ▶₀ #t2.3 )
+                          case insertlalogspkiyes_0_11111121111111
+                          by contradiction /* cyclic */
+                        qed
+                      qed
+                    qed
+                  qed
+                qed
+              next
+                case insertlalogspkcyes_0_111111211111
+                solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #t2.1 )
+                  case p_1_1111112111
+                  solve( State_111111211111111( ~n.3, $la.1, pk.1, $s.1, $ca.1 ) ▶₀ #t2.2 )
+                    case insertlalogspkiyes_0_11111121111111
+                    by contradiction /* cyclic */
+                  qed
+                qed
+              qed
+            qed
+          next
+            case case_2
+            solve( (#t2.1 < #j.1)  ∥ (#t2.1 = #j.1) )
+              case case_1
+              by contradiction /* from formulas */
+            next
+              case case_2
+              solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #j.1 )
+                case insertlalogSpkentityyes_0_212111111
+                solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                  case locklog_0_21211111_case_1
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.1 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspksyes_0_1111112111111
+                      solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                        case insertlalogspkcyes_0_111111211111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_2
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.1 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspksyes_0_1111112111111
+                      solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                        case insertlalogspkcyes_0_111111211111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_3
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.1 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspksyes_0_1111112111111
+                      solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                        case insertlalogspkcyes_0_111111211111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_4
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.1 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #j.1 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #j.1 )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspksyes_0_1111112111111
+                      solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                        case insertlalogspkcyes_0_111111211111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                qed
+              next
+                case insertlalogspkcyes_0_111111211111
+                solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                  case p_1_1111112111
+                  solve( State_111111211111111( ~n.1, $la.1, pk.1, $s.1, $ca.1 ) ▶₀ #t2.1 )
+                    case insertlalogspkiyes_0_11111121111111
+                    by contradiction /* cyclic */
+                  qed
+                qed
+              qed
+            qed
+          next
+            case case_3
+            solve( (#t2.1 < #t2.2)  ∥ (#t2.1 = #t2.2) )
+              case case_1
+              by contradiction /* from formulas */
+            next
+              case case_2
+              solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #t2.1 )
+                case insertlalogSpkentityyes_0_212111111
+                solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #t2.1 )
+                  case locklog_0_21211111_case_1
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j.1 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_2
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j.1 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_3
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j.1 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_4
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j.1 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                qed
+              next
+                case insertlalogspkcyes_0_111111211111
+                solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #t2.1 )
+                  case p_1_1111112111
+                  solve( State_111111211111111( ~n.3, $la.1, pk.1, $s.1, $ca.1 ) ▶₀ #t2.2 )
+                    case insertlalogspkiyes_0_11111121111111
+                    by contradiction /* cyclic */
+                  qed
+                qed
+              qed
+            qed
+          qed
+        qed
+      next
+        case unlocklog_0_111121112111
+        by solve( State_111121112111( $la.1, ~n, x2, pk.1, $s.1 ) ▶₀ #t2 )
+      qed
+    qed
+  next
+    case eventDishonestLAla_0_1111211121
+    solve( State_1111211121( $la, lock, x2, pk, $s ) ▶₀ #i )
+      case lookuplalogspksasx_0_111121112
+      solve( Unlock_2( '2', ~n, 'log' ) @ #t2 )
+        case unlocklog_0_111121111111
+        by solve( State_111121111111( x1, x2.1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+      next
+        case unlocklog_0_111121111211
+        by solve( State_111121111211( x1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+      next
+        case unlocklog_0_111121112111
+        solve( State_111121112111( $la.1, ~n, x2.1, pk.1, $s.1 ) ▶₀ #t2 )
+          case eventTestLAlaspk_0_11112111211
+          solve( (#j.1 < #t2.2)  ∥ (#j.1 = #t2.2)  ∥ (#vr.4 < #j.1) )
+            case case_1
+            solve( (#t2.2 < #t2.1)  ∥ (#t2.2 = #t2.1) )
+              case case_1
+              by contradiction /* from formulas */
+            next
+              case case_2
+              solve( Insert( <$la, 'log', $s, pk, 's1'>, x2 ) @ #t2.1 )
+                case insertlalogSpkentityyes_0_212111111
+                solve( State_212111111( $id, $s, 's1', $la, pk, lock ) ▶₀ #t2.1 )
+                  case locklog_0_21211111_case_1
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_2
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_3
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_4
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                qed
+              next
+                case insertlalogspksyes_0_1111112111111
+                solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #t2.1 )
+                  case insertlalogspkcyes_0_111111211111
+                  by contradiction /* cyclic */
+                qed
+              qed
+            qed
+          next
+            case case_2
+            solve( (#t2.1 < #j.1)  ∥ (#t2.1 = #j.1) )
+              case case_1
+              by contradiction /* from formulas */
+            next
+              case case_2
+              solve( Insert( <$la, 'log', $s, pk, 's1'>, x2 ) @ #j.1 )
+                case insertlalogSpkentityyes_0_212111111
+                solve( State_212111111( $id, $s, 's1', $la, pk, lock ) ▶₀ #j )
+                  case locklog_0_21211111_case_1
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.1 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j.1 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id.1, $s, 'c1', $la, pk, lock ) ▶₀ #j.1 )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_2
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.1 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j.1 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id.1, $s, 'c1', $la, pk, lock ) ▶₀ #j.1 )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_3
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.1 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j.1 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id.1, $s, 'c1', $la, pk, lock ) ▶₀ #j.1 )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_4
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.1 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j.1 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id.1, $s, 'c1', $la, pk, lock ) ▶₀ #j.1 )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j.1 )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                qed
+              next
+                case insertlalogspksyes_0_1111112111111
+                solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                  case insertlalogspkcyes_0_111111211111
+                  by contradiction /* cyclic */
+                qed
+              qed
+            qed
+          next
+            case case_3
+            solve( (#t2.1 < #t2.2)  ∥ (#t2.1 = #t2.2) )
+              case case_1
+              by contradiction /* from formulas */
+            next
+              case case_2
+              solve( Insert( <$la, 'log', $s, pk, 's1'>, x2 ) @ #t2.1 )
+                case insertlalogSpkentityyes_0_212111111
+                solve( State_212111111( $id, $s, 's1', $la, pk, lock ) ▶₀ #t2.1 )
+                  case locklog_0_21211111_case_1
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_2
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_3
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_4
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                qed
+              next
+                case insertlalogspksyes_0_1111112111111
+                solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #t2.1 )
+                  case insertlalogspkcyes_0_111111211111
+                  by contradiction /* cyclic */
+                qed
+              qed
+            qed
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma accLA_tLA_min:
+  all-traces
+  "∀ la #i.
+    (DishonestLA( la ) @ #i) ⇒
+    (¬(∃ la.1 #i.1.
+        (DishonestLA( la.1 ) @ #i.1) ∧ ((la.1 = la) ∧ (¬(la = la.1)))))"
+/*
+guarded formula characterizing all counter-examples:
+"∃ la #i.
+  (DishonestLA( la ) @ #i)
+ ∧
+  ∃ la.1 #i.1. (DishonestLA( la.1 ) @ #i.1) ∧ (la.1 = la) ∧ ¬(la = la.1)"
+*/
+simplify
+by contradiction /* from formulas */
+
+lemma accLA_tLA_uniq:
+  all-traces
+  "∀ la #i. (DishonestLA( la ) @ #i) ⇒ (∃ #i.1. Corrupted( la ) @ #i.1)"
+/*
+guarded formula characterizing all counter-examples:
+"∃ la #i.
+  (DishonestLA( la ) @ #i) ∧ ∀ #i.1. (Corrupted( la ) @ #i.1) ⇒ ⊥"
+*/
+simplify
+solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+  case locklog_0_111211
+  solve( DishonestLA( la ) @ #i )
+    case eventDishonestLAla_0_1111211112
+    solve( State_1111211112( x1, $la, lock, pk, $s ) ▶₀ #i )
+      case lookuplalogspksasx_1_111121111
+      solve( Unlock_2( '2', ~n, 'log' ) @ #t2 )
+        case unlocklog_0_111121111111
+        by solve( State_111121111111( x1.1, x2, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+      next
+        case unlocklog_0_111121111211
+        solve( State_111121111211( x1.1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+          case eventTestLAlaspk_0_11112111121
+          solve( (#t2.1 < #t2.2)  ∥ (#t2.1 = #t2.2) )
+            case case_1
+            by contradiction /* from formulas */
+          next
+            case case_2
+            solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #t2.1 )
+              case insertlalogSpkentityyes_0_212111111
+              solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #t2.1 )
+                case locklog_0_21211111_case_1
+                by contradiction /* from formulas */
+              next
+                case locklog_0_21211111_case_2
+                by contradiction /* from formulas */
+              next
+                case locklog_0_21211111_case_3
+                by contradiction /* from formulas */
+              next
+                case locklog_0_21211111_case_4
+                by contradiction /* from formulas */
+              qed
+            next
+              case insertlalogspkcyes_0_111111211111
+              solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #t2.1 )
+                case p_1_1111112111
+                solve( State_111111211111111( ~n.3, $la.1, pk.1, $s.1, $ca.1 ) ▶₀ #t2.2 )
+                  case insertlalogspkiyes_0_11111121111111
+                  by contradiction /* cyclic */
+                qed
+              qed
+            qed
+          qed
+        qed
+      next
+        case unlocklog_0_111121112111
+        by solve( State_111121112111( $la.1, ~n, x2, pk.1, $s.1 ) ▶₀ #t2 )
+      qed
+    qed
+  next
+    case eventDishonestLAla_0_1111211121
+    solve( State_1111211121( $la, lock, x2, pk, $s ) ▶₀ #i )
+      case lookuplalogspksasx_0_111121112
+      solve( Unlock_2( '2', ~n, 'log' ) @ #t2 )
+        case unlocklog_0_111121111111
+        by solve( State_111121111111( x1, x2.1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+      next
+        case unlocklog_0_111121111211
+        by solve( State_111121111211( x1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+      next
+        case unlocklog_0_111121112111
+        solve( State_111121112111( $la.1, ~n, x2.1, pk.1, $s.1 ) ▶₀ #t2 )
+          case eventTestLAlaspk_0_11112111211
+          solve( (#t2.1 < #t2.2)  ∥ (#t2.1 = #t2.2) )
+            case case_1
+            by contradiction /* from formulas */
+          next
+            case case_2
+            solve( Insert( <$la, 'log', $s, pk, 's1'>, x2 ) @ #t2.1 )
+              case insertlalogSpkentityyes_0_212111111
+              solve( State_212111111( $id, $s, 's1', $la, pk, lock ) ▶₀ #t2.1 )
+                case locklog_0_21211111_case_1
+                by contradiction /* from formulas */
+              next
+                case locklog_0_21211111_case_2
+                by contradiction /* from formulas */
+              next
+                case locklog_0_21211111_case_3
+                by contradiction /* from formulas */
+              next
+                case locklog_0_21211111_case_4
+                by contradiction /* from formulas */
+              qed
+            next
+              case insertlalogspksyes_0_1111112111111
+              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #t2.1 )
+                case insertlalogspkcyes_0_111111211111
+                by contradiction /* cyclic */
+              qed
+            qed
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma accLA_tLA_inj:
+  all-traces "⊤"
+/*
+guarded formula characterizing all counter-examples:
+"⊥"
+*/
+by contradiction /* from formulas */
+
+lemma accLA_tLA_single:
+  exists-trace
+  "∃ la #i.
+    (DishonestLA( la ) @ #i) ∧
+    (∀ la.1 #i.1. (DishonestLA( la.1 ) @ #i.1) ⇒ (la.1 = la))"
+/*
+guarded formula characterizing all satisfying traces:
+"∃ la #i.
+  (DishonestLA( la ) @ #i)
+ ∧
+  ∀ la.1 #i.1. (DishonestLA( la.1 ) @ #i.1) ⇒ la.1 = la"
+*/
+simplify
+solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+  case locklog_0_111211
+  solve( DishonestLA( la ) @ #i )
+    case eventDishonestLAla_0_1111211112
+    solve( State_1111211112( x1, $la, lock, pk, $s ) ▶₀ #i )
+      case lookuplalogspksasx_1_111121111
+      solve( Unlock_2( '2', ~n, 'log' ) @ #t2 )
+        case unlocklog_0_111121111211
+        solve( State_111121111211( x1.1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+          case eventTestLAlaspk_0_11112111121
+          solve( (#t2.1 < #t2.2)  ∥ (#t2.1 = #t2.2) )
+            case case_2
+            solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #t2.1 )
+              case insertlalogSpkentityyes_0_212111111
+              solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #t2.1 )
+                case locklog_0_21211111_case_1
+                solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                  case insertlalogSpkentityyes_0_212111111
+                  SOLVED // trace found
+                qed
+              qed
+            qed
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma acc_tCA_suff:
+  exists-trace
+  "∃ ca #i.
+    ((DishonestCA( ca ) @ #i) ∧
+     (∀ ca.1 #i.1. (DishonestCA( ca.1 ) @ #i.1) ⇒ (ca.1 = ca))) ∧
+    ((∀ a #i.1. (Corrupted( a ) @ #i.1) ⇒ (a = ca)) ∧
+     (¬(∃ la #i.1. DishonestLA( la ) @ #i.1)))"
+/*
+guarded formula characterizing all satisfying traces:
+"∃ ca #i.
+  (DishonestCA( ca ) @ #i)
+ ∧
+  (∀ ca.1 #i.1. (DishonestCA( ca.1 ) @ #i.1) ⇒ ca.1 = ca) ∧
+  (∀ a #i.1. (Corrupted( a ) @ #i.1) ⇒ a = ca) ∧
+  (∀ la #i.1. (DishonestLA( la ) @ #i.1) ⇒ ⊥)"
+*/
+simplify
+solve( State_1111121112( lock, pk, $s, $ca ) ▶₀ #i )
+  case lookupcaproofOfIDspkasignored_1_111112111
+  solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+    case locklog_0_111211
+    solve( Unlock_1( '1', ~n, 'testCA' ) @ #t2 )
+      case unlocktestCA_0_111112111211
+      solve( State_111112111211( ~n, pk.1, $s.1, $ca.1 ) ▶₀ #t2 )
+        case eventTestCAcaspk_0_11111211121
+        solve( !KU( sign(skca($ca), <pk, $s>) ) @ #vk )
+          case c_sign
+          solve( !KU( skca($ca) ) @ #vk.1 )
+            case outcskcaca_0_21111
+            solve( State_2111( $ca ) ▶₀ #vr.9 )
+              case incCAcorruptca_1_211
+              SOLVED // trace found
+            qed
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma acc_tLA_suff:
+  exists-trace
+  "∃ la #i.
+    ((DishonestLA( la ) @ #i) ∧
+     (∀ la.1 #i.1. (DishonestLA( la.1 ) @ #i.1) ⇒ (la.1 = la))) ∧
+    ((∀ a #i.1. (Corrupted( a ) @ #i.1) ⇒ (a = la)) ∧
+     (¬(∃ ca #i.1. DishonestCA( ca ) @ #i.1)))"
+/*
+guarded formula characterizing all satisfying traces:
+"∃ la #i.
+  (DishonestLA( la ) @ #i)
+ ∧
+  (∀ la.1 #i.1. (DishonestLA( la.1 ) @ #i.1) ⇒ la.1 = la) ∧
+  (∀ a #i.1. (Corrupted( a ) @ #i.1) ⇒ a = la) ∧
+  (∀ ca #i.1. (DishonestCA( ca ) @ #i.1) ⇒ ⊥)"
+*/
+simplify
+solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+  case locklog_0_111211
+  solve( DishonestLA( la ) @ #i )
+    case eventDishonestLAla_0_1111211112
+    solve( State_1111211112( x1, $la, lock, pk, $s ) ▶₀ #i )
+      case lookuplalogspksasx_1_111121111
+      solve( Unlock_2( '2', ~n, 'log' ) @ #t2 )
+        case unlocklog_0_111121111211
+        solve( State_111121111211( x1.1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+          case eventTestLAlaspk_0_11112111121
+          solve( (#t2.1 < #t2.2)  ∥ (#t2.1 = #t2.2) )
+            case case_2
+            solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #t2.1 )
+              case insertlalogSpkentityyes_0_212111111
+              solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #t2.1 )
+                case locklog_0_21211111_case_1
+                solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                  case insertlalogSpkentityyes_0_212111111
+                  SOLVED // trace found
+                qed
+              qed
+            qed
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma acc_verif_empty:
+  all-traces
+  "(¬((∃ ca #i. DishonestCA( ca ) @ #i) ∨
+      (∃ la #i. DishonestLA( la ) @ #i))) ⇒
+   ((¬(∃ la s pk #i.
+        (TestLA( la, s, pk ) @ #i) ∧
+        (¬(∃ #j #k.
+            (((Insert( <la, 'log', s, pk, 'c1'>, 'yes' ) @ #j) ∧ (#j < #i)) ∧
+             (Insert( <la, 'log', s, pk, 's1'>, 'yes' ) @ #k)) ∧
+            (#k < #i))))) ∧
+    (¬(∃ ca s pk #i.
+        (TestCA( ca, s, pk ) @ #i) ∧
+        (¬(∃ #j. HonestRegister( s, ca, pk ) @ #j)))))"
+/*
+guarded formula characterizing all counter-examples:
+"(∀ ca #i. (DishonestCA( ca ) @ #i) ⇒ ⊥) ∧
+ (∀ la #i. (DishonestLA( la ) @ #i) ⇒ ⊥) ∧
+ (((∃ la s pk #i.
+     (TestLA( la, s, pk ) @ #i)
+    ∧
+     ∀ #j #k.
+      (Insert( <la, 'log', s, pk, 'c1'>, 'yes' ) @ #j) ∧
+      (Insert( <la, 'log', s, pk, 's1'>, 'yes' ) @ #k)
+     ⇒
+      ((¬(#j < #i)) ∨ (¬(#k < #i)))) ∨
+   (∃ ca s pk #i.
+     (TestCA( ca, s, pk ) @ #i)
+    ∧
+     ∀ #j. (HonestRegister( s, ca, pk ) @ #j) ⇒ ⊥)))"
+*/
+simplify
+solve( (∃ la s pk #i.
+         (TestLA( la, s, pk ) @ #i)
+        ∧
+         ∀ #j #k.
+          (Insert( <la, 'log', s, pk, 'c1'>, 'yes' ) @ #j) ∧
+          (Insert( <la, 'log', s, pk, 's1'>, 'yes' ) @ #k)
+         ⇒
+          ((¬(#j < #i)) ∨ (¬(#k < #i))))  ∥
+       (∃ ca s pk #i.
+         (TestCA( ca, s, pk ) @ #i)
+        ∧
+         ∀ #j. (HonestRegister( s, ca, pk ) @ #j) ⇒ ⊥) )
+  case case_1
+  solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+    case locklog_0_111211
+    solve( TestLA( la, s, pk ) @ #i )
+      case eventTestLAlaspk_0_11112111111
+      solve( State_11112111111( x1, x2, $la, lock, pk, $s ) ▶₀ #i )
+        case eventHonestLA_0_1111211111
+        solve( Unlock_2( '2', ~n, 'log' ) @ #t2 )
+          case unlocklog_0_111121111111
+          solve( State_111121111111( x1.1, x2.1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+            case eventTestLAlaspk_0_11112111111
+            solve( (#t2.2 < #t2.4)  ∥ (#t2.2 = #t2.4) )
+              case case_1
+              by contradiction /* from formulas */
+            next
+              case case_2
+              solve( (#t2.1 < #t2.3)  ∥ (#t2.1 = #t2.3) )
+                case case_1
+                by contradiction /* from formulas */
+              next
+                case case_2
+                solve( Insert( <$la, 'log', $s, pk, 's1'>, x2 ) @ #t2.1 )
+                  case insertlalogSpkentityyes_0_212111111
+                  solve( State_212111111( $id, $s, 's1', $la, pk, lock ) ▶₀ #t2.1 )
+                    case locklog_0_21211111_case_1
+                    solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #t2.3 )
+                        case insertlalogSpkentityyes_0_212111111
+                        by contradiction /* from formulas */
+                      next
+                        case insertlalogspkcyes_0_111111211111
+                        by contradiction /* from formulas */
+                      qed
+                    qed
+                  next
+                    case locklog_0_21211111_case_2
+                    solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #t2.3 )
+                        case insertlalogSpkentityyes_0_212111111
+                        by contradiction /* from formulas */
+                      next
+                        case insertlalogspkcyes_0_111111211111
+                        by contradiction /* from formulas */
+                      qed
+                    qed
+                  next
+                    case locklog_0_21211111_case_3
+                    solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #t2.3 )
+                        case insertlalogSpkentityyes_0_212111111
+                        by contradiction /* from formulas */
+                      next
+                        case insertlalogspkcyes_0_111111211111
+                        by contradiction /* from formulas */
+                      qed
+                    qed
+                  next
+                    case locklog_0_21211111_case_4
+                    solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #t2.3 )
+                        case insertlalogSpkentityyes_0_212111111
+                        by contradiction /* from formulas */
+                      next
+                        case insertlalogspkcyes_0_111111211111
+                        by contradiction /* from formulas */
+                      qed
+                    qed
+                  qed
+                next
+                  case insertlalogspksyes_0_1111112111111
+                  solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #t2.1 )
+                    case insertlalogspkcyes_0_111111211111
+                    by contradiction /* from formulas */
+                  qed
+                qed
+              qed
+            qed
+          qed
+        next
+          case unlocklog_0_111121111211
+          by solve( State_111121111211( x1.1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+        next
+          case unlocklog_0_111121112111
+          by solve( State_111121112111( $la.1, ~n, x2.1, pk.1, $s.1 ) ▶₀ #t2 )
+        qed
+      qed
+    next
+      case eventTestLAlaspk_0_11112111121
+      solve( State_11112111121( x1, $la, lock, pk, $s ) ▶₀ #i )
+        case eventDishonestLAla_0_1111211112
+        by contradiction /* from formulas */
+      qed
+    next
+      case eventTestLAlaspk_0_11112111211
+      solve( State_11112111211( $la, lock, x2, pk, $s ) ▶₀ #i )
+        case eventDishonestLAla_0_1111211121
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case case_2
+  solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+    case locklog_0_111211
+    solve( TestCA( ca, s, pk ) @ #i )
+      case eventTestCAcaspk_0_11111211111
+      solve( State_11111211111( ignored, lock, pk, $s, $ca ) ▶₀ #i )
+        case eventHonestCAca_0_1111121111
+        solve( Unlock_1( '1', ~n, 'testCA' ) @ #t2 )
+          case unlocktestCA_0_111112111111
+          solve( State_111112111111( ignored.1, ~n, pk.1, $s.1, $ca.1 ) ▶₀ #t2 )
+            case eventTestCAcaspk_0_11111211111
+            solve( (#t2.1 < #t2.2)  ∥ (#t2.1 = #t2.2) )
+              case case_1
+              by contradiction /* from formulas */
+            next
+              case case_2
+              solve( !KU( sign(skca($ca), <pk, $s>) ) @ #vk )
+                case c_sign
+                solve( !KU( skca($ca) ) @ #vk.1 )
+                  case outcskcaca_0_21111
+                  solve( State_2111( $ca ) ▶₀ #vr.9 )
+                    case incCAcorruptca_1_211
+                    solve( Insert( <$ca, 'proofOfID', $s, pk>, ignored ) @ #t2.1 )
+                      case insertcaproofOfIDspkskSyes_0_11111111111111
+                      solve( State_11111111111111( $ca.1, $s, skS, $ca ) ▶₀ #t2.1 )
+                        case p_1_1111111111
+                        by contradiction /* from formulas */
+                      qed
+                    qed
+                  next
+                    case incCAcorruptca_3_211
+                    solve( Insert( <$ca, 'proofOfID', $s, pk>, ignored ) @ #t2.1 )
+                      case insertcaproofOfIDspkskSyes_0_11111111111111
+                      solve( State_11111111111111( $ca.1, $s, skS, $ca ) ▶₀ #t2.1 )
+                        case p_1_1111111111
+                        by contradiction /* from formulas */
+                      qed
+                    qed
+                  qed
+                qed
+              next
+                case outsignskcacapkskSs_0_1111111111111111
+                by contradiction /* from formulas */
+              qed
+            qed
+          qed
+        next
+          case unlocktestCA_0_111112111211
+          by solve( State_111112111211( ~n, pk.1, $s.1, $ca.1 ) ▶₀ #t2 )
+        qed
+      qed
+    next
+      case eventTestCAcaspk_0_11111211121
+      solve( State_11111211121( lock, pk, $s, $ca ) ▶₀ #i )
+        case eventDishonestCAca_0_1111121112
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+qed
+
+lemma acc_tCA_verif_nonempty:
+  all-traces
+  "∀ ca #i.
+    (DishonestCA( ca ) @ #i) ⇒
+    (¬((¬(∃ la s pk #i.1.
+           (TestLA( la, s, pk ) @ #i.1) ∧
+           (¬(∃ #j #k.
+               (((Insert( <la, 'log', s, pk, 'c1'>, 'yes' ) @ #j) ∧ (#j < #i.1)) ∧
+                (Insert( <la, 'log', s, pk, 's1'>, 'yes' ) @ #k)) ∧
+               (#k < #i.1))))) ∧
+       (¬(∃ ca.1 s pk #i.1.
+           (TestCA( ca.1, s, pk ) @ #i.1) ∧
+           (¬(∃ #j. HonestRegister( s, ca.1, pk ) @ #j))))))"
+/*
+guarded formula characterizing all counter-examples:
+"∃ ca #i.
+  (DishonestCA( ca ) @ #i)
+ ∧
+  (∀ la s pk #i.1.
+    (TestLA( la, s, pk ) @ #i.1)
+   ⇒
+    ∃ #j #k.
+     (Insert( <la, 'log', s, pk, 'c1'>, 'yes' ) @ #j) ∧
+     (Insert( <la, 'log', s, pk, 's1'>, 'yes' ) @ #k)
+    ∧
+     (#j < #i.1) ∧ (#k < #i.1)) ∧
+  (∀ ca.1 s pk #i.1.
+    (TestCA( ca.1, s, pk ) @ #i.1)
+   ⇒
+    ∃ #j. (HonestRegister( s, ca.1, pk ) @ #j))"
+*/
+simplify
+solve( State_1111121112( lock, pk, $s, $ca ) ▶₀ #i )
+  case lookupcaproofOfIDspkasignored_1_111112111
+  solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+    case locklog_0_111211
+    solve( Unlock_1( '1', ~n, 'testCA' ) @ #t2 )
+      case unlocktestCA_0_111112111111
+      by solve( State_111112111111( ignored, ~n, pk.1, $s.1, $ca.1 ) ▶₀ #t2 )
+    next
+      case unlocktestCA_0_111112111211
+      solve( State_111112111211( ~n, pk.1, $s.1, $ca.1 ) ▶₀ #t2 )
+        case eventTestCAcaspk_0_11111211121
+        solve( !Semistate_11111111111( $ca.1 ) ▶₀ #j )
+          case inca_0_1111111
+          solve( !KU( sign(skca($ca), <pk(~n.1), $s>) ) @ #vk )
+            case c_sign
+            solve( !KU( skca($ca) ) @ #vk.6 )
+              case outcskcaca_0_21111
+              solve( State_2111( $ca ) ▶₀ #vr.11 )
+                case incCAcorruptca_1_211
+                solve( !KU( pk(~n.1) ) @ #vk.8 )
+                  case c_pk
+                  by solve( !KU( ~n.1 ) @ #vk.12 )
+                next
+                  case insertcaproofOfIDspkskSyes_0_11111111111111
+                  by contradiction /* cyclic */
+                next
+                  case outsignskcacapkskSs_0_1111111111111111
+                  by contradiction /* cyclic */
+                qed
+              next
+                case incCAcorruptca_3_211
+                solve( !KU( pk(~n.1) ) @ #vk.8 )
+                  case c_pk
+                  by solve( !KU( ~n.1 ) @ #vk.12 )
+                next
+                  case insertcaproofOfIDspkskSyes_0_11111111111111
+                  by contradiction /* cyclic */
+                next
+                  case outsignskcacapkskSs_0_1111111111111111
+                  by contradiction /* cyclic */
+                qed
+              qed
+            qed
+          next
+            case outsignskcacapkskSs_0_1111111111111111
+            by contradiction /* cyclic */
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma acc_tLA_verif_nonempty:
+  all-traces
+  "∀ la #i.
+    (DishonestLA( la ) @ #i) ⇒
+    (¬((¬(∃ la.1 s pk #i.1.
+           (TestLA( la.1, s, pk ) @ #i.1) ∧
+           (¬(∃ #j #k.
+               (((Insert( <la.1, 'log', s, pk, 'c1'>, 'yes' ) @ #j) ∧ (#j < #i.1)) ∧
+                (Insert( <la.1, 'log', s, pk, 's1'>, 'yes' ) @ #k)) ∧
+               (#k < #i.1))))) ∧
+       (¬(∃ ca s pk #i.1.
+           (TestCA( ca, s, pk ) @ #i.1) ∧
+           (¬(∃ #j. HonestRegister( s, ca, pk ) @ #j))))))"
+/*
+guarded formula characterizing all counter-examples:
+"∃ la #i.
+  (DishonestLA( la ) @ #i)
+ ∧
+  (∀ la.1 s pk #i.1.
+    (TestLA( la.1, s, pk ) @ #i.1)
+   ⇒
+    ∃ #j #k.
+     (Insert( <la.1, 'log', s, pk, 'c1'>, 'yes' ) @ #j) ∧
+     (Insert( <la.1, 'log', s, pk, 's1'>, 'yes' ) @ #k)
+    ∧
+     (#j < #i.1) ∧ (#k < #i.1)) ∧
+  (∀ ca s pk #i.1.
+    (TestCA( ca, s, pk ) @ #i.1) ⇒ ∃ #j. (HonestRegister( s, ca, pk ) @ #j))"
+*/
+simplify
+solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+  case locklog_0_111211
+  solve( DishonestLA( la ) @ #i )
+    case eventDishonestLAla_0_1111211112
+    solve( State_1111211112( x1, $la, lock, pk, $s ) ▶₀ #i )
+      case lookuplalogspksasx_1_111121111
+      solve( Unlock_2( '2', ~n, 'log' ) @ #t2 )
+        case unlocklog_0_111121111111
+        by solve( State_111121111111( x1.1, x2, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+      next
+        case unlocklog_0_111121111211
+        solve( State_111121111211( x1.1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+          case eventTestLAlaspk_0_11112111121
+          solve( (#j < #t2.2)  ∥ (#j = #t2.2)  ∥ (#vr.5 < #j) )
+            case case_1
+            solve( (#t2.2 < #t2.1)  ∥ (#t2.2 = #t2.1) )
+              case case_1
+              by contradiction /* from formulas */
+            next
+              case case_2
+              solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #t2.1 )
+                case insertlalogSpkentityyes_0_212111111
+                solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #t2.1 )
+                  case locklog_0_21211111_case_1
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        next
+                          case case_3
+                          by contradiction /* cyclic */
+                        qed
+                      next
+                        case locklog_0_21211111_case_2
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      next
+                        case locklog_0_21211111_case_3
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      next
+                        case locklog_0_21211111_case_4
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        solve( State_111111211111111( ~n.1, $la.1, pk.1, $s.1, $ca.1 ) ▶₀ #t2.3 )
+                          case insertlalogspkiyes_0_11111121111111
+                          by contradiction /* cyclic */
+                        qed
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_2
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      next
+                        case locklog_0_21211111_case_2
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        next
+                          case case_3
+                          by contradiction /* cyclic */
+                        qed
+                      next
+                        case locklog_0_21211111_case_3
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      next
+                        case locklog_0_21211111_case_4
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        solve( State_111111211111111( ~n.1, $la.1, pk.1, $s.1, $ca.1 ) ▶₀ #t2.3 )
+                          case insertlalogspkiyes_0_11111121111111
+                          by contradiction /* cyclic */
+                        qed
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_3
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      next
+                        case locklog_0_21211111_case_2
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      next
+                        case locklog_0_21211111_case_3
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        next
+                          case case_3
+                          by contradiction /* cyclic */
+                        qed
+                      next
+                        case locklog_0_21211111_case_4
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        solve( State_111111211111111( ~n.1, $la.1, pk.1, $s.1, $ca.1 ) ▶₀ #t2.3 )
+                          case insertlalogspkiyes_0_11111121111111
+                          by contradiction /* cyclic */
+                        qed
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_4
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      next
+                        case locklog_0_21211111_case_2
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      next
+                        case locklog_0_21211111_case_3
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        qed
+                      next
+                        case locklog_0_21211111_case_4
+                        solve( ((#vr.9 < #vr.18) ∧
+                                (∃ #t2.
+                                  (Unlock_5( '5', ~n.4, 'log' ) @ #t2)
+                                 ∧
+                                  (#vr.9 < #t2) ∧
+                                  (#t2 < #vr.18) ∧
+                                  (∀ #t0 pp. (Unlock( pp, ~n.4, 'log' ) @ #t0) ⇒ #t0 = #t2) ∧
+                                  (∀ pp lpp #t0.
+                                    (Lock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t0 = #vr.9) ∨ (#t2 < #t0))) ∧
+                                  (∀ pp lpp #t0.
+                                    (Unlock( pp, lpp, 'log' ) @ #t0)
+                                   ⇒
+                                    ((#t0 < #vr.9) ∨ (#t2 < #t0) ∨ (#t2 = #t0)))))  ∥
+                               (#vr.18 < #vr.9)  ∥ (#vr.9 = #vr.18) )
+                          case case_1
+                          by contradiction /* cyclic */
+                        next
+                          case case_2
+                          solve( State_2121111111( $id.2, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.3 )
+                            case insertlalogSpkentityyes_0_212111111
+                            solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                              case insertlalogSpkentityyes_0_212111111
+                              solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                                case locklog_0_21211111_case_1
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_2
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_3
+                                by contradiction /* cyclic */
+                              next
+                                case locklog_0_21211111_case_4
+                                by contradiction /* cyclic */
+                              qed
+                            next
+                              case insertlalogspksyes_0_1111112111111
+                              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                                case insertlalogspkcyes_0_111111211111
+                                by contradiction /* cyclic */
+                              qed
+                            qed
+                          qed
+                        next
+                          case case_3
+                          by contradiction /* cyclic */
+                        qed
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        solve( State_111111211111111( ~n.1, $la.1, pk.1, $s.1, $ca.1 ) ▶₀ #t2.3 )
+                          case insertlalogspkiyes_0_11111121111111
+                          by contradiction /* cyclic */
+                        qed
+                      qed
+                    qed
+                  qed
+                qed
+              next
+                case insertlalogspkcyes_0_111111211111
+                solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #t2.1 )
+                  case p_1_1111112111
+                  solve( State_111111211111111( ~n.3, $la.1, pk.1, $s.1, $ca.1 ) ▶₀ #t2.2 )
+                    case insertlalogspkiyes_0_11111121111111
+                    by contradiction /* cyclic */
+                  qed
+                qed
+              qed
+            qed
+          next
+            case case_2
+            solve( (#t2.1 < #j)  ∥ (#t2.1 = #j) )
+              case case_1
+              by contradiction /* from formulas */
+            next
+              case case_2
+              solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #j )
+                case insertlalogSpkentityyes_0_212111111
+                solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                  case locklog_0_21211111_case_1
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.1 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspksyes_0_1111112111111
+                      solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                        case insertlalogspkcyes_0_111111211111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_2
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.1 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspksyes_0_1111112111111
+                      solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                        case insertlalogspkcyes_0_111111211111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_3
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.1 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspksyes_0_1111112111111
+                      solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                        case insertlalogspkcyes_0_111111211111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_4
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.1 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 's1'>, 'yes' ) @ #k )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id.1, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspksyes_0_1111112111111
+                      solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                        case insertlalogspkcyes_0_111111211111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                qed
+              next
+                case insertlalogspkcyes_0_111111211111
+                solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                  case p_1_1111112111
+                  solve( State_111111211111111( ~n.1, $la.1, pk.1, $s.1, $ca.1 ) ▶₀ #t2.1 )
+                    case insertlalogspkiyes_0_11111121111111
+                    by contradiction /* cyclic */
+                  qed
+                qed
+              qed
+            qed
+          next
+            case case_3
+            solve( (#t2.1 < #t2.2)  ∥ (#t2.1 = #t2.2) )
+              case case_1
+              by contradiction /* from formulas */
+            next
+              case case_2
+              solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #t2.1 )
+                case insertlalogSpkentityyes_0_212111111
+                solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #t2.1 )
+                  case locklog_0_21211111_case_1
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_2
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_3
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_4
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                qed
+              next
+                case insertlalogspkcyes_0_111111211111
+                solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #t2.1 )
+                  case p_1_1111112111
+                  solve( State_111111211111111( ~n.3, $la.1, pk.1, $s.1, $ca.1 ) ▶₀ #t2.2 )
+                    case insertlalogspkiyes_0_11111121111111
+                    by contradiction /* cyclic */
+                  qed
+                qed
+              qed
+            qed
+          qed
+        qed
+      next
+        case unlocklog_0_111121112111
+        by solve( State_111121112111( $la.1, ~n, x2, pk.1, $s.1 ) ▶₀ #t2 )
+      qed
+    qed
+  next
+    case eventDishonestLAla_0_1111211121
+    solve( State_1111211121( $la, lock, x2, pk, $s ) ▶₀ #i )
+      case lookuplalogspksasx_0_111121112
+      solve( Unlock_2( '2', ~n, 'log' ) @ #t2 )
+        case unlocklog_0_111121111111
+        by solve( State_111121111111( x1, x2.1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+      next
+        case unlocklog_0_111121111211
+        by solve( State_111121111211( x1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+      next
+        case unlocklog_0_111121112111
+        solve( State_111121112111( $la.1, ~n, x2.1, pk.1, $s.1 ) ▶₀ #t2 )
+          case eventTestLAlaspk_0_11112111211
+          solve( (#k < #t2.2)  ∥ (#k = #t2.2)  ∥ (#vr.4 < #k) )
+            case case_1
+            solve( (#t2.2 < #t2.1)  ∥ (#t2.2 = #t2.1) )
+              case case_1
+              by contradiction /* from formulas */
+            next
+              case case_2
+              solve( Insert( <$la, 'log', $s, pk, 's1'>, x2 ) @ #t2.1 )
+                case insertlalogSpkentityyes_0_212111111
+                solve( State_212111111( $id, $s, 's1', $la, pk, lock ) ▶₀ #t2.1 )
+                  case locklog_0_21211111_case_1
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_2
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_3
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_4
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                qed
+              next
+                case insertlalogspksyes_0_1111112111111
+                solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #t2.1 )
+                  case insertlalogspkcyes_0_111111211111
+                  by contradiction /* cyclic */
+                qed
+              qed
+            qed
+          next
+            case case_2
+            solve( (#t2.1 < #k)  ∥ (#t2.1 = #k) )
+              case case_1
+              by contradiction /* from formulas */
+            next
+              case case_2
+              solve( Insert( <$la, 'log', $s, pk, 's1'>, x2 ) @ #k )
+                case insertlalogSpkentityyes_0_212111111
+                solve( State_212111111( $id, $s, 's1', $la, pk, lock ) ▶₀ #k )
+                  case locklog_0_21211111_case_1
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.1 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_2
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.1 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_3
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.1 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_4
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.1 ) ▶₀ #t2.1 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                qed
+              next
+                case insertlalogspksyes_0_1111112111111
+                solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #k )
+                  case insertlalogspkcyes_0_111111211111
+                  by contradiction /* cyclic */
+                qed
+              qed
+            qed
+          next
+            case case_3
+            solve( (#t2.1 < #t2.2)  ∥ (#t2.1 = #t2.2) )
+              case case_1
+              by contradiction /* from formulas */
+            next
+              case case_2
+              solve( Insert( <$la, 'log', $s, pk, 's1'>, x2 ) @ #t2.1 )
+                case insertlalogSpkentityyes_0_212111111
+                solve( State_212111111( $id, $s, 's1', $la, pk, lock ) ▶₀ #t2.1 )
+                  case locklog_0_21211111_case_1
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_2
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_3
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                next
+                  case locklog_0_21211111_case_4
+                  solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                    case insertlalogSpkentityyes_0_212111111
+                    solve( Insert( <$la, 'log', $s, pk, 'c1'>, 'yes' ) @ #j )
+                      case insertlalogSpkentityyes_0_212111111
+                      solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #j )
+                        case locklog_0_21211111_case_1
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_2
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_3
+                        by contradiction /* cyclic */
+                      next
+                        case locklog_0_21211111_case_4
+                        by contradiction /* cyclic */
+                      qed
+                    next
+                      case insertlalogspkcyes_0_111111211111
+                      solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #j )
+                        case p_1_1111112111
+                        by contradiction /* cyclic */
+                      qed
+                    qed
+                  qed
+                qed
+              next
+                case insertlalogspksyes_0_1111112111111
+                solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #t2.1 )
+                  case insertlalogspkcyes_0_111111211111
+                  by contradiction /* cyclic */
+                qed
+              qed
+            qed
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma acc_tCA_min:
+  all-traces
+  "∀ ca #i.
+    (DishonestCA( ca ) @ #i) ⇒
+    ((¬(∃ ca.1 #i.1.
+         (DishonestCA( ca.1 ) @ #i.1) ∧ ((ca.1 = ca) ∧ (¬(ca = ca.1))))) ∧
+     (¬(∃ la #i.1. (DishonestLA( la ) @ #i.1) ∧ ((la = ca) ∧ (¬(ca = la))))))"
+/*
+guarded formula characterizing all counter-examples:
+"∃ ca #i.
+  (DishonestCA( ca ) @ #i)
+ ∧
+  ((∃ ca.1 #i.1.
+     (DishonestCA( ca.1 ) @ #i.1) ∧ (ca.1 = ca) ∧ ¬(ca = ca.1)) ∨
+   (∃ la #i.1. (DishonestLA( la ) @ #i.1) ∧ (la = ca) ∧ ¬(ca = la)))"
+*/
+simplify
+solve( (∃ ca.1 #i.
+         (DishonestCA( ca.1 ) @ #i) ∧ (ca.1 = $ca) ∧ ¬($ca = ca.1))  ∥
+       (∃ la #i. (DishonestLA( la ) @ #i) ∧ (la = $ca) ∧ ¬($ca = la)) )
+  case case_1
+  by contradiction /* from formulas */
+next
+  case case_2
+  by contradiction /* from formulas */
+qed
+
+lemma acc_tLA_min:
+  all-traces
+  "∀ la #i.
+    (DishonestLA( la ) @ #i) ⇒
+    ((¬(∃ ca #i.1.
+         (DishonestCA( ca ) @ #i.1) ∧ ((ca = la) ∧ (¬(la = ca))))) ∧
+     (¬(∃ la.1 #i.1.
+         (DishonestLA( la.1 ) @ #i.1) ∧ ((la.1 = la) ∧ (¬(la = la.1))))))"
+/*
+guarded formula characterizing all counter-examples:
+"∃ la #i.
+  (DishonestLA( la ) @ #i)
+ ∧
+  ((∃ ca #i.1. (DishonestCA( ca ) @ #i.1) ∧ (ca = la) ∧ ¬(la = ca)) ∨
+   (∃ la.1 #i.1.
+     (DishonestLA( la.1 ) @ #i.1) ∧ (la.1 = la) ∧ ¬(la = la.1)))"
+*/
+simplify
+solve( (∃ ca #i. (DishonestCA( ca ) @ #i) ∧ (ca = la) ∧ ¬(la = ca))  ∥
+       (∃ la.1 #i. (DishonestLA( la.1 ) @ #i) ∧ (la.1 = la) ∧ ¬(la = la.1)) )
+  case case_1
+  by contradiction /* from formulas */
+next
+  case case_2
+  by contradiction /* from formulas */
+qed
+
+lemma acc_tCA_uniq:
+  all-traces
+  "∀ ca #i. (DishonestCA( ca ) @ #i) ⇒ (∃ #i.1. Corrupted( ca ) @ #i.1)"
+/*
+guarded formula characterizing all counter-examples:
+"∃ ca #i.
+  (DishonestCA( ca ) @ #i) ∧ ∀ #i.1. (Corrupted( ca ) @ #i.1) ⇒ ⊥"
+*/
+simplify
+solve( State_1111121112( lock, pk, $s, $ca ) ▶₀ #i )
+  case lookupcaproofOfIDspkasignored_1_111112111
+  solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+    case locklog_0_111211
+    solve( Unlock_1( '1', ~n, 'testCA' ) @ #t2 )
+      case unlocktestCA_0_111112111111
+      by solve( State_111112111111( ignored, ~n, pk.1, $s.1, $ca.1 ) ▶₀ #t2 )
+    next
+      case unlocktestCA_0_111112111211
+      solve( State_111112111211( ~n, pk.1, $s.1, $ca.1 ) ▶₀ #t2 )
+        case eventTestCAcaspk_0_11111211121
+        solve( !KU( sign(skca($ca), <pk, $s>) ) @ #vk )
+          case c_sign
+          solve( !KU( skca($ca) ) @ #vk.1 )
+            case outcskcaca_0_21111
+            by contradiction /* from formulas */
+          qed
+        next
+          case outsignskcacapkskSs_0_1111111111111111
+          by contradiction /* cyclic */
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma acc_tLA_uniq:
+  all-traces
+  "∀ la #i. (DishonestLA( la ) @ #i) ⇒ (∃ #i.1. Corrupted( la ) @ #i.1)"
+/*
+guarded formula characterizing all counter-examples:
+"∃ la #i.
+  (DishonestLA( la ) @ #i) ∧ ∀ #i.1. (Corrupted( la ) @ #i.1) ⇒ ⊥"
+*/
+simplify
+solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+  case locklog_0_111211
+  solve( DishonestLA( la ) @ #i )
+    case eventDishonestLAla_0_1111211112
+    solve( State_1111211112( x1, $la, lock, pk, $s ) ▶₀ #i )
+      case lookuplalogspksasx_1_111121111
+      solve( Unlock_2( '2', ~n, 'log' ) @ #t2 )
+        case unlocklog_0_111121111111
+        by solve( State_111121111111( x1.1, x2, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+      next
+        case unlocklog_0_111121111211
+        solve( State_111121111211( x1.1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+          case eventTestLAlaspk_0_11112111121
+          solve( (#t2.1 < #t2.2)  ∥ (#t2.1 = #t2.2) )
+            case case_1
+            by contradiction /* from formulas */
+          next
+            case case_2
+            solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #t2.1 )
+              case insertlalogSpkentityyes_0_212111111
+              solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #t2.1 )
+                case locklog_0_21211111_case_1
+                by contradiction /* from formulas */
+              next
+                case locklog_0_21211111_case_2
+                by contradiction /* from formulas */
+              next
+                case locklog_0_21211111_case_3
+                by contradiction /* from formulas */
+              next
+                case locklog_0_21211111_case_4
+                by contradiction /* from formulas */
+              qed
+            next
+              case insertlalogspkcyes_0_111111211111
+              solve( State_111111211111( lock, $la, pk, $s, $ca ) ▶₀ #t2.1 )
+                case p_1_1111112111
+                solve( State_111111211111111( ~n.3, $la.1, pk.1, $s.1, $ca.1 ) ▶₀ #t2.2 )
+                  case insertlalogspkiyes_0_11111121111111
+                  by contradiction /* cyclic */
+                qed
+              qed
+            qed
+          qed
+        qed
+      next
+        case unlocklog_0_111121112111
+        by solve( State_111121112111( $la.1, ~n, x2, pk.1, $s.1 ) ▶₀ #t2 )
+      qed
+    qed
+  next
+    case eventDishonestLAla_0_1111211121
+    solve( State_1111211121( $la, lock, x2, pk, $s ) ▶₀ #i )
+      case lookuplalogspksasx_0_111121112
+      solve( Unlock_2( '2', ~n, 'log' ) @ #t2 )
+        case unlocklog_0_111121111111
+        by solve( State_111121111111( x1, x2.1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+      next
+        case unlocklog_0_111121111211
+        by solve( State_111121111211( x1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+      next
+        case unlocklog_0_111121112111
+        solve( State_111121112111( $la.1, ~n, x2.1, pk.1, $s.1 ) ▶₀ #t2 )
+          case eventTestLAlaspk_0_11112111211
+          solve( (#t2.1 < #t2.2)  ∥ (#t2.1 = #t2.2) )
+            case case_1
+            by contradiction /* from formulas */
+          next
+            case case_2
+            solve( Insert( <$la, 'log', $s, pk, 's1'>, x2 ) @ #t2.1 )
+              case insertlalogSpkentityyes_0_212111111
+              solve( State_212111111( $id, $s, 's1', $la, pk, lock ) ▶₀ #t2.1 )
+                case locklog_0_21211111_case_1
+                by contradiction /* from formulas */
+              next
+                case locklog_0_21211111_case_2
+                by contradiction /* from formulas */
+              next
+                case locklog_0_21211111_case_3
+                by contradiction /* from formulas */
+              next
+                case locklog_0_21211111_case_4
+                by contradiction /* from formulas */
+              qed
+            next
+              case insertlalogspksyes_0_1111112111111
+              solve( State_1111112111111( lock, $la, pk, $s, $ca ) ▶₀ #t2.1 )
+                case insertlalogspkcyes_0_111111211111
+                by contradiction /* cyclic */
+              qed
+            qed
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma acc_tCA_inj:
+  all-traces "⊤"
+/*
+guarded formula characterizing all counter-examples:
+"⊥"
+*/
+by contradiction /* from formulas */
+
+lemma acc_tLA_inj:
+  all-traces "⊤"
+/*
+guarded formula characterizing all counter-examples:
+"⊥"
+*/
+by contradiction /* from formulas */
+
+lemma acc_tCA_single:
+  exists-trace
+  "∃ ca #i.
+    ((DishonestCA( ca ) @ #i) ∧
+     (∀ ca.1 #i.1. (DishonestCA( ca.1 ) @ #i.1) ⇒ (ca.1 = ca))) ∧
+    (¬(∃ la #i.1. DishonestLA( la ) @ #i.1))"
+/*
+guarded formula characterizing all satisfying traces:
+"∃ ca #i.
+  (DishonestCA( ca ) @ #i)
+ ∧
+  (∀ ca.1 #i.1. (DishonestCA( ca.1 ) @ #i.1) ⇒ ca.1 = ca) ∧
+  (∀ la #i.1. (DishonestLA( la ) @ #i.1) ⇒ ⊥)"
+*/
+simplify
+solve( State_1111121112( lock, pk, $s, $ca ) ▶₀ #i )
+  case lookupcaproofOfIDspkasignored_1_111112111
+  solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+    case locklog_0_111211
+    solve( Unlock_1( '1', ~n, 'testCA' ) @ #t2 )
+      case unlocktestCA_0_111112111211
+      solve( State_111112111211( ~n, pk.1, $s.1, $ca.1 ) ▶₀ #t2 )
+        case eventTestCAcaspk_0_11111211121
+        solve( !KU( sign(skca($ca), <pk, $s>) ) @ #vk )
+          case c_sign
+          solve( !KU( skca($ca) ) @ #vk.1 )
+            case outcskcaca_0_21111
+            solve( State_2111( $ca ) ▶₀ #vr.9 )
+              case incCAcorruptca_1_211
+              SOLVED // trace found
+            qed
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma acc_tLA_single:
+  exists-trace
+  "∃ la #i.
+    ((DishonestLA( la ) @ #i) ∧
+     (∀ la.1 #i.1. (DishonestLA( la.1 ) @ #i.1) ⇒ (la.1 = la))) ∧
+    (¬(∃ ca #i.1. DishonestCA( ca ) @ #i.1))"
+/*
+guarded formula characterizing all satisfying traces:
+"∃ la #i.
+  (DishonestLA( la ) @ #i)
+ ∧
+  (∀ la.1 #i.1. (DishonestLA( la.1 ) @ #i.1) ⇒ la.1 = la) ∧
+  (∀ ca #i.1. (DishonestCA( ca ) @ #i.1) ⇒ ⊥)"
+*/
+simplify
+solve( State_1112111( lock, lock.1 ) ▶₀ #t )
+  case locklog_0_111211
+  solve( DishonestLA( la ) @ #i )
+    case eventDishonestLAla_0_1111211112
+    solve( State_1111211112( x1, $la, lock, pk, $s ) ▶₀ #i )
+      case lookuplalogspksasx_1_111121111
+      solve( Unlock_2( '2', ~n, 'log' ) @ #t2 )
+        case unlocklog_0_111121111211
+        solve( State_111121111211( x1.1, $la.1, ~n, pk.1, $s.1 ) ▶₀ #t2 )
+          case eventTestLAlaspk_0_11112111121
+          solve( (#t2.1 < #t2.2)  ∥ (#t2.1 = #t2.2) )
+            case case_2
+            solve( Insert( <$la, 'log', $s, pk, 'c1'>, x1 ) @ #t2.1 )
+              case insertlalogSpkentityyes_0_212111111
+              solve( State_212111111( $id, $s, 'c1', $la, pk, lock ) ▶₀ #t2.1 )
+                case locklog_0_21211111_case_1
+                solve( State_2121111111( $id.1, S, entity, $la.1, pk.1, ~n.3 ) ▶₀ #t2.2 )
+                  case insertlalogSpkentityyes_0_212111111
+                  SOLVED // trace found
+                qed
+              qed
+            qed
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+predicate: tCA( ca )<=>∃ #i. DishonestCA( ca ) @ #i
+
+predicate: tLA( la )<=>∃ #i. DishonestLA( la ) @ #i
+
+/*
+WARNING: the following wellformedness checks failed!
+
+Wellformedness-error in Process
+  Variable bound twice: $ca.
+
+Accountability (RP check)
+  The specification contains at least one restriction.
+  
+  Please verify manually that your protocol fulfills the following condition:
+  
+  For each case test τ, traces t, t’, and instantiations ρ, ρ’:
+  If τ holds on t with ρ, and τ single-matches with ρ’ on t’, then
+  there exists a trace t’’ such that τ single-matches with ρ on t’’
+  and the parties corrupted in t’’ are the same as the parties
+  corrupted in t’ renamed from rng(ρ’) to rng(ρ).
+
+Message Derivation Checks
+=========================
+
+  The variables of the follwing rule(s) are not derivable from their premises, you may be performing unintended pattern matching.
+
+Rule inca_0_1111111: 
+Failed to derive Variable(s): $ca.1
+
+Rule p_1_1111111111: 
+Failed to derive Variable(s): $ca.1, $s.1, skS.1, $ca.2
+
+Rule insertcaproofOfIDspkskSyes_0_11111111111111: 
+Failed to derive Variable(s): $ca.1, $s.1, skS.1, $ca.2
+
+Rule outsignskcacapkskSs_0_1111111111111111: 
+Failed to derive Variable(s): $ca.1, $s.1, skS.1, $ca.2
+
+Rule inla_0_1111112: 
+Failed to derive Variable(s): $la.1, pk.1, $s.2, $ca.3
+
+Rule p_1_1111112111: 
+Failed to derive Variable(s): lock, $la.1, pk.1, $s.2, $ca.3
+
+Rule insertlalogspkcyes_0_111111211111: 
+Failed to derive Variable(s): lock, $la.1, pk.1, $s.2, $ca.3
+
+Rule insertlalogspksyes_0_1111112111111: 
+Failed to derive Variable(s): lock, $la.1, pk.1, $s.2, $ca.3
+
+Rule insertlalogspkiyes_0_11111121111111: 
+Failed to derive Variable(s): lock, $la.1, pk.1, $s.2, $ca.3
+
+Rule unlocklog_0_111111211111111: 
+Failed to derive Variable(s): lock, $la.1, pk.1, $s.2, $ca.3
+
+Rule locktestCA_0_1111121: 
+Failed to derive Variable(s): lock.1, pk.2, $s.3, $ca.4
+
+Rule lookupcaproofOfIDspkasignored_0_111112111: 
+Failed to derive Variable(s): ignored.1, lock.1, pk.2, $s.3, $ca.4
+
+Rule eventHonestCAca_0_1111121111: 
+Failed to derive Variable(s): ignored.1, lock.1, pk.2, $s.3, $ca.4
+
+Rule eventTestCAcaspk_0_11111211111: 
+Failed to derive Variable(s): ignored.1, lock.1, pk.2, $s.3, $ca.4
+
+Rule unlocktestCA_0_111112111111: 
+Failed to derive Variable(s): ignored.1, lock.1, pk.2, $s.3, $ca.4
+
+Rule lookupcaproofOfIDspkasignored_1_111112111: 
+Failed to derive Variable(s): lock.1, pk.2, $s.3, $ca.4
+
+Rule eventDishonestCAca_0_1111121112: 
+Failed to derive Variable(s): lock.1, pk.2, $s.3, $ca.4
+
+Rule eventTestCAcaspk_0_11111211121: 
+Failed to derive Variable(s): lock.1, pk.2, $s.3, $ca.4
+
+Rule unlocktestCA_0_111112111211: 
+Failed to derive Variable(s): lock.1, pk.2, $s.3, $ca.4
+
+Rule locklog_0_111121: 
+Failed to derive Variable(s): $la.2, lock.2, pk.3, $s.4
+
+Rule lookuplalogspkcasx_0_11112111: 
+Failed to derive Variable(s): x1.1, $la.2, lock.2, pk.3, $s.4
+
+Rule lookuplalogspksasx_0_111121111: 
+Failed to derive Variable(s): x1.1, x2.1, $la.2, lock.2, pk.3, $s.4
+
+Rule eventHonestLA_0_1111211111: 
+Failed to derive Variable(s): x1.1, x2.1, $la.2, lock.2, pk.3, $s.4
+
+Rule eventTestLAlaspk_0_11112111111: 
+Failed to derive Variable(s): x1.1, x2.1, $la.2, lock.2, pk.3, $s.4
+
+Rule unlocklog_0_111121111111: 
+Failed to derive Variable(s): x1.1, x2.1, $la.2, lock.2, pk.3, $s.4
+
+Rule lookuplalogspksasx_1_111121111: 
+Failed to derive Variable(s): x1.1, $la.2, lock.2, pk.3, $s.4
+
+Rule eventDishonestLAla_0_1111211112: 
+Failed to derive Variable(s): x1.1, $la.2, lock.2, pk.3, $s.4
+
+Rule eventTestLAlaspk_0_11112111121: 
+Failed to derive Variable(s): x1.1, $la.2, lock.2, pk.3, $s.4
+
+Rule unlocklog_0_111121111211: 
+Failed to derive Variable(s): x1.1, $la.2, lock.2, pk.3, $s.4
+
+Rule lookuplalogspkcasx_1_11112111: 
+Failed to derive Variable(s): $la.2, lock.2, pk.3, $s.4
+
+Rule lookuplalogspksasx_0_111121112: 
+Failed to derive Variable(s): $la.2, lock.2, x2.2, pk.3, $s.4
+
+Rule eventDishonestLAla_0_1111211121: 
+Failed to derive Variable(s): $la.2, lock.2, x2.2, pk.3, $s.4
+
+Rule eventTestLAlaspk_0_11112111211: 
+Failed to derive Variable(s): $la.2, lock.2, x2.2, pk.3, $s.4
+
+Rule unlocklog_0_111121112111: 
+Failed to derive Variable(s): $la.2, lock.2, x2.2, pk.3, $s.4
+
+Rule lookuplalogspksasx_1_111121112: 
+Failed to derive Variable(s): $la.2, lock.2, pk.3, $s.4
+
+Rule locktestCA_0_11121: 
+Failed to derive Variable(s): lock.3
+
+Rule locklog_0_111211: 
+Failed to derive Variable(s): lock.3, lock.4
+
+Rule eventTerminate_0_1112111: 
+Failed to derive Variable(s): lock.3, lock.4
+
+Rule incCAcorruptca_0_211: 
+Failed to derive Variable(s): x
+
+Rule incCAcorruptca_2_211: 
+Failed to derive Variable(s): x
+
+Rule incCAcorruptca_1_211: 
+Failed to derive Variable(s): $ca.5
+
+Rule incCAcorruptca_3_211: 
+Failed to derive Variable(s): $ca.5
+
+Rule eventCorruptedca_0_2111: 
+Failed to derive Variable(s): $ca.5
+
+Rule outcskcaca_1_21111: 
+Failed to derive Variable(s): $ca.5
+
+Rule outcskcaca_0_21111: 
+Failed to derive Variable(s): $ca.5
+
+Rule outcskcaca_2_21111: 
+Failed to derive Variable(s): $ca.5
+
+Rule inclaLAcorruptid_0_2121: 
+Failed to derive Variable(s): x
+
+Rule inclaLAcorruptid_2_2121: 
+Failed to derive Variable(s): x
+
+Rule inclaLAcorruptid_1_2121: 
+Failed to derive Variable(s): $id.1, $la.3
+
+Rule inclaLAcorruptid_3_2121: 
+Failed to derive Variable(s): $id.1, $la.3
+
+Rule eventCorruptedla_0_21211: 
+Failed to derive Variable(s): $id.1, $la.3
+
+Rule p_1_212111: 
+Failed to derive Variable(s): $id.1, $la.3
+
+Rule incSpkentity_0_2121111: 
+Failed to derive Variable(s): $id.1, $la.3, x.4
+
+Rule incSpkentity_2_2121111: 
+Failed to derive Variable(s): $id.1, $la.3, x.4
+
+Rule incSpkentity_1_2121111: 
+Failed to derive Variable(s): $id.1, S.1, entity.1, $la.3, pk.4
+
+Rule incSpkentity_3_2121111: 
+Failed to derive Variable(s): $id.1, S.1, entity.1, $la.3, pk.4
+
+Rule locklog_0_21211111: 
+Failed to derive Variable(s): $id.1, S.1, entity.1, $la.3, pk.4, lock.5
+
+Rule insertlalogSpkentityyes_0_212111111: 
+Failed to derive Variable(s): $id.1, S.1, entity.1, $la.3, pk.4, lock.5
+
+Rule unlocklog_0_2121111111: 
+Failed to derive Variable(s): $id.1, S.1, entity.1, $la.3, pk.4, lock.5
+*/
+
+/*
+Generated from:
+Tamarin version 1.9.0
+Maude version 3.2.2
+Git revision: c838686f5a3d41b6a355eafd32cc2104ca41809c (with uncommited changes), branch: HEAD
+Compiled at: 2023-10-25 11:27:38.363683988 UTC
+*/
+
+end
+/* Output
+
+==============================================================================
+summary of summaries:
+
+analyzed: examples/accountability/csf21-acc-unbounded/previous/ct.spthy
+
+  output:          examples/accountability/csf21-acc-unbounded/previous/ct.spthy.tmp
+  processing time: 28.80s
+  
+  WARNING: 3 wellformedness check failed!
+           The analysis results might be wrong!
+  
+  accCA_tCA_suff (exists-trace): verified (9 steps)
+  accCA_verif_empty (all-traces): verified (21 steps)
+  accCA_tCA_verif_nonempty (all-traces): verified (19 steps)
+  accCA_tCA_min (all-traces): verified (2 steps)
+  accCA_tCA_uniq (all-traces): verified (10 steps)
+  accCA_tCA_inj (all-traces): verified (1 steps)
+  accCA_tCA_single (exists-trace): verified (9 steps)
+  accLA_tLA_suff (exists-trace): verified (11 steps)
+  accLA_verif_empty (all-traces): verified (55 steps)
+  accLA_tLA_verif_nonempty (all-traces): verified (438 steps)
+  accLA_tLA_min (all-traces): verified (2 steps)
+  accLA_tLA_uniq (all-traces): verified (34 steps)
+  accLA_tLA_inj (all-traces): verified (1 steps)
+  accLA_tLA_single (exists-trace): verified (11 steps)
+  acc_tCA_suff (exists-trace): verified (9 steps)
+  acc_tLA_suff (exists-trace): verified (11 steps)
+  acc_verif_empty (all-traces): verified (57 steps)
+  acc_tCA_verif_nonempty (all-traces): verified (19 steps)
+  acc_tLA_verif_nonempty (all-traces): verified (438 steps)
+  acc_tCA_min (all-traces): verified (4 steps)
+  acc_tLA_min (all-traces): verified (4 steps)
+  acc_tCA_uniq (all-traces): verified (10 steps)
+  acc_tLA_uniq (all-traces): verified (34 steps)
+  acc_tCA_inj (all-traces): verified (1 steps)
+  acc_tLA_inj (all-traces): verified (1 steps)
+  acc_tCA_single (exists-trace): verified (9 steps)
+  acc_tLA_single (exists-trace): verified (11 steps)
+
+==============================================================================
+*/
diff --git a/case-studies-regression/accountability/csf21-acc-unbounded/previous/ocsps-msr-untrusted_analyzed.spthy b/case-studies-regression/accountability/csf21-acc-unbounded/previous/ocsps-msr-untrusted_analyzed.spthy
new file mode 100644
index 000000000..e54e49c39
--- /dev/null
+++ b/case-studies-regression/accountability/csf21-acc-unbounded/previous/ocsps-msr-untrusted_analyzed.spthy
@@ -0,0 +1,576 @@
+theory OCSPS_MSR begin
+
+// Function signature and definition of the equational theory E
+
+functions: extract/1, fst/1, id/1, pair/2, pk/1, sig/2,
+           sk/1[private,destructor], snd/1, true/0, verify/3
+equations:
+    extract(sig(m, sk(i))) = m,
+    fst(<x.1, x.2>) = x.1,
+    id(pk(sk(x))) = x,
+    snd(<x.1, x.2>) = x.2,
+    verify(sig(m, sk(i)), m, pk(sk(i))) = true
+
+
+
+
+
+rule (modulo E) Init:
+   [ ]
+  --[ Responder( $rs ), CA( $ca ) ]->
+   [
+   !RS( $rs, sk($rs), pk(sk($ca)) ), Out( pk(sk($rs)) ),
+   !RSpk( pk(sk($rs)) ), !CApk( pk(sk($ca)) ), !CAsk( sk($ca) )
+   ]
+
+  /* has exactly the trivial AC variant */
+
+rule (modulo E) RS_resp:
+   [ !RS( $rs, skRS, pkCA ), In( cert ), CertStatus( $s, cert, status ) ]
+  --[
+  IsTrue( verify(cert, extract(cert), pkCA) ), Time( $tn ),
+  ValidStatus( <pk(sk($rs)), cert, status, $tn> )
+  ]->
+   [
+   Out( <<pk(sk($rs)), cert, status, $tn>, 
+         sig(<pk(sk($rs)), cert, status, $tn>, skRS)>
+   )
+   ]
+
+  /*
+  rule (modulo AC) RS_resp:
+     [ !RS( $rs, skRS, pkCA ), In( cert ), CertStatus( $s, cert, status ) ]
+    --[
+    IsTrue( z ), Time( $tn ), ValidStatus( <pk(sk($rs)), cert, status, $tn> )
+    ]->
+     [
+     Out( <<pk(sk($rs)), cert, status, $tn>, 
+           sig(<pk(sk($rs)), cert, status, $tn>, skRS)>
+     )
+     ]
+    variants (modulo AC)
+    1. cert  = cert.9
+       pkCA  = pkCA.9
+       z     = verify(cert.9, extract(cert.9), pkCA.9)
+    
+    2. cert  = sig(x.9, sk(x.10))
+       pkCA  = pkCA.11
+       z     = verify(sig(x.9, sk(x.10)), x.9, pkCA.11)
+    
+    3. cert  = sig(x.9, sk(x.10))
+       pkCA  = pk(sk(x.10))
+       z     = true
+  */
+
+rule (modulo E) C_receive:
+   [ In( <<pkRS, cert, status, ts>, resp_sig, server_sig> ), !RSpk( pkRS ) ]
+  --[
+  IsTrue( verify(resp_sig, <pkRS, cert, status, ts>, pkRS) ),
+  IsTrue( verify(server_sig, <pkRS, cert, status, ts>, extract(cert)) )
+  ]->
+   [ C( ts, cert, status ) ]
+
+  /*
+  rule (modulo AC) C_receive:
+     [ In( <<pkRS, cert, status, ts>, resp_sig, server_sig> ), !RSpk( pkRS ) ]
+    --[ IsTrue( z ), IsTrue( z.1 ) ]->
+     [ C( ts, cert, status ) ]
+    variants (modulo AC)
+    1. cert  = cert.9
+       pkRS  = pkRS.9
+       resp_sig
+             = resp_sig.9
+       server_sig
+             = server_sig.9
+       status
+             = status.9
+       ts    = ts.9
+       z     = verify(resp_sig.9, <pkRS.9, cert.9, status.9, ts.9>, pkRS.9)
+       z.1   = verify(server_sig.9, <pkRS.9, cert.9, status.9, ts.9>,
+                      extract(cert.9))
+    
+    2. cert  = x.9
+       pkRS  = pk(sk(x.10))
+       resp_sig
+             = sig(<pk(sk(x.10)), x.9, x.11, x.12>, sk(x.10))
+       server_sig
+             = server_sig.13
+       status
+             = x.11
+       ts    = x.12
+       z     = true
+       z.1   = verify(server_sig.13, <pk(sk(x.10)), x.9, x.11, x.12>,
+                      extract(x.9))
+    
+    3. cert  = sig(x.9, sk(x.10))
+       pkRS  = pkRS.11
+       resp_sig
+             = resp_sig.11
+       server_sig
+             = server_sig.11
+       status
+             = status.11
+       ts    = ts.11
+       z     = verify(resp_sig.11,
+                      <pkRS.11, sig(x.9, sk(x.10)), status.11, ts.11>, pkRS.11)
+       z.1   = verify(server_sig.11,
+                      <pkRS.11, sig(x.9, sk(x.10)), status.11, ts.11>, x.9)
+    
+    4. cert  = sig(x.9, sk(x.10))
+       pkRS  = pk(sk(x.11))
+       resp_sig
+             = sig(<pk(sk(x.11)), sig(x.9, sk(x.10)), x.12, x.13>, sk(x.11))
+       server_sig
+             = server_sig.14
+       status
+             = x.12
+       ts    = x.13
+       z     = true
+       z.1   = verify(server_sig.14,
+                      <pk(sk(x.11)), sig(x.9, sk(x.10)), x.12, x.13>, x.9)
+    
+    5. cert  = sig(pk(sk(x.9)), sk(x.10))
+       pkRS  = x.11
+       resp_sig
+             = resp_sig.15
+       server_sig
+             = sig(<x.11, sig(pk(sk(x.9)), sk(x.10)), x.13, x.14>, sk(x.9))
+       status
+             = x.13
+       ts    = x.14
+       z     = verify(resp_sig.15,
+                      <x.11, sig(pk(sk(x.9)), sk(x.10)), x.13, x.14>, x.11)
+       z.1   = true
+    
+    6. cert  = sig(pk(sk(x.9)), sk(x.10))
+       pkRS  = pk(sk(x.11))
+       resp_sig
+             = sig(<pk(sk(x.11)), sig(pk(sk(x.9)), sk(x.10)), x.12, x.13>, sk(x.11))
+       server_sig
+             = sig(<pk(sk(x.11)), sig(pk(sk(x.9)), sk(x.10)), x.12, x.13>, sk(x.9))
+       status
+             = x.12
+       ts    = x.13
+       z     = true
+       z.1   = true
+  */
+
+rule (modulo E) C_judge_good:
+   [ C( ts, cert, 'good' ) ] --[ Judged( ts, cert ) ]-> [ ]
+
+  /* has exactly the trivial AC variant */
+
+rule (modulo E) C_judge_revoked:
+   [ C( ts, cert, 'revoked' ) ]
+  --[ Blame( id(extract(cert)) ), Judged( ts, cert ) ]->
+   [ ]
+
+  /*
+  rule (modulo AC) C_judge_revoked:
+     [ C( ts, cert, 'revoked' ) ] --[ Blame( z ), Judged( ts, cert ) ]-> [ ]
+    variants (modulo AC)
+    1. cert  = cert.6
+       z     = id(extract(cert.6))
+    
+    2. cert  = sig(x.7, sk(x.8))
+       z     = id(x.7)
+    
+    3. cert  = sig(pk(sk(z.7)), sk(x.9))
+       z     = z.7
+  */
+
+rule (modulo E) S_init:
+   [ !CAsk( skCA ) ]
+  --[ Server( $s ), Secret( sig(pk(sk($s)), skCA), sk($s) ) ]->
+   [
+   CertStatus( $s, sig(pk(sk($s)), skCA), 'good' ), Out( pk(sk($s)) ),
+   Out( sig(pk(sk($s)), skCA) ), !S( $s, sig(pk(sk($s)), skCA) )
+   ]
+
+  /* has exactly the trivial AC variant */
+
+rule (modulo E) S_honest:
+   [
+   In( <<pkRS, cert, status, t>, resp_sig> ), !S( $s, cert ), !RSpk( pkRS )
+   ]
+  --[ IsTrue( verify(resp_sig, <pkRS, cert, status, t>, pkRS) ) ]->
+   [
+   Out( <<pkRS, cert, status, t>, resp_sig, 
+         sig(<pkRS, cert, status, t>, sk($s))>
+   )
+   ]
+
+  /*
+  rule (modulo AC) S_honest:
+     [
+     In( <<pkRS, cert, status, t>, resp_sig> ), !S( $s, cert ), !RSpk( pkRS )
+     ]
+    --[ IsTrue( z ) ]->
+     [
+     Out( <<pkRS, cert, status, t>, resp_sig, 
+           sig(<pkRS, cert, status, t>, sk($s))>
+     )
+     ]
+    variants (modulo AC)
+    1. cert  = cert.8
+       pkRS  = pkRS.8
+       resp_sig
+             = resp_sig.8
+       status
+             = status.8
+       t     = t.8
+       z     = verify(resp_sig.8, <pkRS.8, cert.8, status.8, t.8>, pkRS.8)
+    
+    2. cert  = x.8
+       pkRS  = pk(sk(x.9))
+       resp_sig
+             = sig(<pk(sk(x.9)), x.8, x.10, x.11>, sk(x.9))
+       status
+             = x.10
+       t     = x.11
+       z     = true
+  */
+
+rule (modulo E) S_corrupt:
+   [ CertStatus( $s, cert, 'good' ) ]
+  --[ Corrupted( $s ), Time( $tn ), NewTime( $tn ), Revealed( sk($s) ) ]->
+   [ CertStatus( $s, cert, 'revoked' ), Out( sk($s) ) ]
+
+  /* has exactly the trivial AC variant */
+
+rule (modulo E) RS_corrupt:
+   [ !RS( $rs, skRS, pkCS ) ] --[ Corrupted( $rs ) ]-> [ Out( skRS ) ]
+
+  /* has exactly the trivial AC variant */
+
+restriction isTrue:
+  "∀ #i t. (IsTrue( t ) @ #i) ⇒ (t = true)"
+  // safety formula
+
+restriction clockGuideTime:
+  "∀ ts #t1 #t3.
+    (((Time( ts ) @ #t1) ∧ (Time( ts ) @ #t3)) ∧ (#t1 < #t3)) ⇒
+    (∀ ts2 #t2.
+      (((Time( ts2 ) @ #t2) ∧ (#t1 < #t2)) ∧ (#t2 < #t3)) ⇒ (ts2 = ts))"
+  // safety formula
+
+restriction NewTime:
+  "∀ ts #i #j.
+    ((NewTime( ts ) @ #i) ∧ (Time( ts ) @ #j)) ⇒ ((#i < #j) ∨ (#i = #j))"
+  // safety formula
+
+restriction CA_single_registration:
+  "∀ c cp skS #i #j.
+    ((Secret( c, skS ) @ #i) ∧ (Secret( cp, skS ) @ #j)) ⇒ (#i = #j)"
+  // safety formula
+
+restriction one_role:
+  "¬(∃ x #i #j. (Responder( x ) @ #i) ∧ (Server( x ) @ #j))"
+  // safety formula
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+lemma acc_blamed_suff:
+  exists-trace
+  "∃ x #i.
+    ((Blame( x ) @ #i) ∧ (∀ x.1 #i.1. (Blame( x.1 ) @ #i.1) ⇒ (x.1 = x))) ∧
+    (∀ a #i.1. (Corrupted( a ) @ #i.1) ⇒ (a = x))"
+/*
+guarded formula characterizing all satisfying traces:
+"∃ x #i.
+  (Blame( x ) @ #i)
+ ∧
+  (∀ x.1 #i.1. (Blame( x.1 ) @ #i.1) ⇒ x.1 = x) ∧
+  (∀ a #i.1. (Corrupted( a ) @ #i.1) ⇒ a = x)"
+*/
+simplify
+solve( C( ts, cert, 'revoked' ) ▶₀ #i )
+  case C_receive
+  solve( !KU( sig(pk(sk(x)), sk(x.1)) ) @ #vk.4 )
+    case S_init
+    solve( !KU( sig(<pk(sk($rs)), sig(pk(sk($s)), sk($ca)), 'revoked', ts>,
+                    sk($rs))
+           ) @ #vk.9 )
+      case RS_resp
+      solve( !KU( sig(<pk(sk($rs)), sig(pk(sk($s)), sk($ca)), 'revoked', $tn>,
+                      sk($s))
+             ) @ #vk.10 )
+        case S_honest
+        solve( !KU( pk(sk($rs)) ) @ #vk.8 )
+          case Init
+          SOLVED // trace found
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma acc_verif_empty:
+  all-traces
+  "(¬(∃ x #i. Blame( x ) @ #i)) ⇒
+   (¬(∃ c sk t #i #j #k #l.
+       ((((Judged( t, c ) @ #i) ∧ (Secret( c, sk ) @ #j)) ∧
+         (Revealed( sk ) @ #k)) ∧
+        (Time( t ) @ #l)) ∧
+       (#k < #l)))"
+/*
+guarded formula characterizing all counter-examples:
+"(∀ x #i. (Blame( x ) @ #i) ⇒ ⊥) ∧
+ (∃ c sk t #i #j #k #l.
+   (Judged( t, c ) @ #i) ∧
+   (Secret( c, sk ) @ #j) ∧
+   (Revealed( sk ) @ #k) ∧
+   (Time( t ) @ #l)
+  ∧
+   #k < #l)"
+*/
+simplify
+solve( !CAsk( skCA ) ▶₀ #j )
+  case Init
+  solve( CertStatus( $s, cert, 'good' ) ▶₀ #k )
+    case S_init
+    solve( Judged( t, sig(pk(sk($s)), sk($ca)) ) @ #i )
+      case C_judge_good
+      solve( C( t, sig(pk(sk($s)), sk($ca)), 'good' ) ▶₀ #i )
+        case C_receive
+        solve( Time( t ) @ #l )
+          case RS_resp
+          solve( !RS( $rs, skRS, pk(sk(x)) ) ▶₀ #l )
+            case Init
+            solve( CertStatus( $s.1, sig(x, sk($ca.1)), status ) ▶₂ #l )
+              case S_corrupt
+              solve( !KU( sig(<pk(sk($rs.1)), sig(pk(sk($s)), sk($ca)), 'good', $tn>,
+                              sk($rs.1))
+                     ) @ #vk.9 )
+                case c_sig
+                solve( !KU( sk($rs.1) ) @ #vk.12 )
+                  case RS_corrupt
+                  solve( !KU( sig(<pk(sk($rs.1)), sig(pk(sk($s)), sk($ca)), 'good', $tn>,
+                                  sk($s))
+                         ) @ #vk.11 )
+                    case S_honest
+                    solve( !KU( pk(sk($rs.1)) ) @ #vk.7 )
+                      case Init
+                      solve( !KU( sig(pk(sk($s)), sk($ca)) ) @ #vk.9 )
+                        case S_init
+                        solve( !KU( sig(pk(sk($s.1)), sk($ca.1)) ) @ #vk.13 )
+                          case S_init
+                          SOLVED // trace found
+                        qed
+                      qed
+                    qed
+                  qed
+                qed
+              qed
+            qed
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma acc_blamed_verif_nonempty:
+  all-traces
+  "∀ x #i.
+    (Blame( x ) @ #i) ⇒
+    (¬(¬(∃ c sk t #i.1 #j #k #l.
+          ((((Judged( t, c ) @ #i.1) ∧ (Secret( c, sk ) @ #j)) ∧
+            (Revealed( sk ) @ #k)) ∧
+           (Time( t ) @ #l)) ∧
+          (#k < #l))))"
+/*
+guarded formula characterizing all counter-examples:
+"∃ x #i.
+  (Blame( x ) @ #i)
+ ∧
+  ∀ c sk t #i.1 #j #k #l.
+   (Judged( t, c ) @ #i.1) ∧
+   (Secret( c, sk ) @ #j) ∧
+   (Revealed( sk ) @ #k) ∧
+   (Time( t ) @ #l)
+  ⇒
+   ¬(#k < #l)"
+*/
+simplify
+solve( C( ts, cert, 'revoked' ) ▶₀ #i )
+  case C_receive
+  solve( !KU( sig(pk(sk(x)), sk(x.1)) ) @ #vk.4 )
+    case S_init
+    solve( !KU( sig(<pk(sk($rs)), sig(pk(sk($s)), sk($ca)), 'revoked', ts>,
+                    sk($rs))
+           ) @ #vk.9 )
+      case c_sig
+      solve( !KU( sk($rs) ) @ #vk.11 )
+        case RS_corrupt
+        solve( !KU( sig(<pk(sk($rs)), sig(pk(sk($s)), sk($ca)), 'revoked', ts>,
+                        sk($s))
+               ) @ #vk.11 )
+          case S_honest
+          solve( !KU( pk(sk($rs)) ) @ #vk.9 )
+            case Init
+            SOLVED // trace found
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma acc_blamed_min:
+  all-traces
+  "∀ x #i.
+    (Blame( x ) @ #i) ⇒
+    (¬(∃ x.1 #i.1. (Blame( x.1 ) @ #i.1) ∧ ((x.1 = x) ∧ (¬(x = x.1)))))"
+/*
+guarded formula characterizing all counter-examples:
+"∃ x #i.
+  (Blame( x ) @ #i)
+ ∧
+  ∃ x.1 #i.1. (Blame( x.1 ) @ #i.1) ∧ (x.1 = x) ∧ ¬(x = x.1)"
+*/
+simplify
+by contradiction /* from formulas */
+
+lemma acc_blamed_uniq:
+  all-traces "∀ x #i. (Blame( x ) @ #i) ⇒ (∃ #i.1. Corrupted( x ) @ #i.1)"
+/*
+guarded formula characterizing all counter-examples:
+"∃ x #i. (Blame( x ) @ #i) ∧ ∀ #i.1. (Corrupted( x ) @ #i.1) ⇒ ⊥"
+*/
+simplify
+solve( C( ts, cert, 'revoked' ) ▶₀ #i )
+  case C_receive
+  solve( !KU( sig(pk(sk(x)), sk(x.1)) ) @ #vk.4 )
+    case S_init
+    solve( !KU( sig(<pk(sk($rs)), sig(pk(sk($s)), sk($ca)), 'revoked', ts>,
+                    sk($rs))
+           ) @ #vk.9 )
+      case c_sig
+      solve( !KU( sk($rs) ) @ #vk.11 )
+        case RS_corrupt
+        solve( !KU( sig(<pk(sk($rs)), sig(pk(sk($s)), sk($ca)), 'revoked', ts>,
+                        sk($s))
+               ) @ #vk.11 )
+          case S_honest
+          solve( !KU( pk(sk($rs)) ) @ #vk.9 )
+            case Init
+            SOLVED // trace found
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma acc_blamed_inj:
+  all-traces "⊤"
+/*
+guarded formula characterizing all counter-examples:
+"⊥"
+*/
+by contradiction /* from formulas */
+
+lemma acc_blamed_single:
+  exists-trace
+  "∃ x #i.
+    (Blame( x ) @ #i) ∧ (∀ x.1 #i.1. (Blame( x.1 ) @ #i.1) ⇒ (x.1 = x))"
+/*
+guarded formula characterizing all satisfying traces:
+"∃ x #i. (Blame( x ) @ #i) ∧ ∀ x.1 #i.1. (Blame( x.1 ) @ #i.1) ⇒ x.1 = x"
+*/
+simplify
+solve( C( ts, cert, 'revoked' ) ▶₀ #i )
+  case C_receive
+  solve( !KU( sig(pk(sk(x)), sk(x.1)) ) @ #vk.4 )
+    case S_init
+    solve( !KU( sig(<pk(sk($rs)), sig(pk(sk($s)), sk($ca)), 'revoked', ts>,
+                    sk($rs))
+           ) @ #vk.9 )
+      case RS_resp
+      solve( !KU( sig(<pk(sk($rs)), sig(pk(sk($s)), sk($ca)), 'revoked', $tn>,
+                      sk($s))
+             ) @ #vk.10 )
+        case S_honest
+        solve( !KU( pk(sk($rs)) ) @ #vk.8 )
+          case Init
+          SOLVED // trace found
+        qed
+      qed
+    qed
+  qed
+qed
+
+predicate: blamed( x )<=>∃ #i. Blame( x ) @ #i
+
+/*
+WARNING: the following wellformedness checks failed!
+
+Accountability (RP check)
+  The specification contains at least one restriction.
+  The specification contains public names.
+  At least one case test can be instantiated with non-public names.
+  
+  Please verify manually that your protocol fulfills the following condition:
+  
+  For each case test τ, traces t, t’, and instantiations ρ, ρ’:
+  If τ holds on t with ρ, and τ single-matches with ρ’ on t’, then
+  there exists a trace t’’ such that τ single-matches with ρ on t’’
+  and the parties corrupted in t’’ are the same as the parties
+  corrupted in t’ renamed from rng(ρ’) to rng(ρ).
+*/
+
+/*
+Generated from:
+Tamarin version 1.9.0
+Maude version 3.2.2
+Git revision: c838686f5a3d41b6a355eafd32cc2104ca41809c (with uncommited changes), branch: HEAD
+Compiled at: 2023-10-25 11:27:38.363683988 UTC
+*/
+
+end
+/* Output
+
+==============================================================================
+summary of summaries:
+
+analyzed: examples/accountability/csf21-acc-unbounded/previous/ocsps-msr-untrusted.spthy
+
+  output:          examples/accountability/csf21-acc-unbounded/previous/ocsps-msr-untrusted.spthy.tmp
+  processing time: 1.45s
+  
+  WARNING: 1 wellformedness check failed!
+           The analysis results might be wrong!
+  
+  acc_blamed_suff (exists-trace): verified (7 steps)
+  acc_verif_empty (all-traces): falsified - found trace (15 steps)
+  acc_blamed_verif_nonempty (all-traces): falsified - found trace (8 steps)
+  acc_blamed_min (all-traces): verified (2 steps)
+  acc_blamed_uniq (all-traces): falsified - found trace (8 steps)
+  acc_blamed_inj (all-traces): verified (1 steps)
+  acc_blamed_single (exists-trace): verified (7 steps)
+
+==============================================================================
+*/
diff --git a/case-studies-regression/accountability/csf21-acc-unbounded/previous/ocsps-msr_analyzed.spthy b/case-studies-regression/accountability/csf21-acc-unbounded/previous/ocsps-msr_analyzed.spthy
new file mode 100644
index 000000000..22d035f2c
--- /dev/null
+++ b/case-studies-regression/accountability/csf21-acc-unbounded/previous/ocsps-msr_analyzed.spthy
@@ -0,0 +1,639 @@
+theory OCSPS_MSR begin
+
+// Function signature and definition of the equational theory E
+
+functions: extract/1, fst/1, id/1, pair/2, pk/1, sig/2,
+           sk/1[private,destructor], snd/1, true/0, verify/3
+equations:
+    extract(sig(m, sk(i))) = m,
+    fst(<x.1, x.2>) = x.1,
+    id(pk(sk(x))) = x,
+    snd(<x.1, x.2>) = x.2,
+    verify(sig(m, sk(i)), m, pk(sk(i))) = true
+
+
+
+
+
+rule (modulo E) Init:
+   [ ]
+  --[ Responder( $rs ), CA( $ca ) ]->
+   [
+   !RS( $rs, sk($rs), pk(sk($ca)) ), Out( pk(sk($rs)) ),
+   !RSpk( pk(sk($rs)) ), !CApk( pk(sk($ca)) ), !CAsk( sk($ca) )
+   ]
+
+  /* has exactly the trivial AC variant */
+
+rule (modulo E) RS_resp:
+   [ !RS( $rs, skRS, pkCA ), In( cert ), CertStatus( $s, cert, status ) ]
+  --[
+  IsTrue( verify(cert, extract(cert), pkCA) ), Time( $tn ),
+  ValidStatus( <pk(sk($rs)), cert, status, $tn> )
+  ]->
+   [
+   Out( <<pk(sk($rs)), cert, status, $tn>, 
+         sig(<pk(sk($rs)), cert, status, $tn>, skRS)>
+   )
+   ]
+
+  /*
+  rule (modulo AC) RS_resp:
+     [ !RS( $rs, skRS, pkCA ), In( cert ), CertStatus( $s, cert, status ) ]
+    --[
+    IsTrue( z ), Time( $tn ), ValidStatus( <pk(sk($rs)), cert, status, $tn> )
+    ]->
+     [
+     Out( <<pk(sk($rs)), cert, status, $tn>, 
+           sig(<pk(sk($rs)), cert, status, $tn>, skRS)>
+     )
+     ]
+    variants (modulo AC)
+    1. cert  = cert.9
+       pkCA  = pkCA.9
+       z     = verify(cert.9, extract(cert.9), pkCA.9)
+    
+    2. cert  = sig(x.9, sk(x.10))
+       pkCA  = pkCA.11
+       z     = verify(sig(x.9, sk(x.10)), x.9, pkCA.11)
+    
+    3. cert  = sig(x.9, sk(x.10))
+       pkCA  = pk(sk(x.10))
+       z     = true
+  */
+
+rule (modulo E) C_receive:
+   [ In( <<pkRS, cert, status, ts>, resp_sig, server_sig> ), !RSpk( pkRS ) ]
+  --[
+  IsTrue( verify(resp_sig, <pkRS, cert, status, ts>, pkRS) ),
+  IsTrue( verify(server_sig, <pkRS, cert, status, ts>, extract(cert)) )
+  ]->
+   [ C( ts, cert, status ) ]
+
+  /*
+  rule (modulo AC) C_receive:
+     [ In( <<pkRS, cert, status, ts>, resp_sig, server_sig> ), !RSpk( pkRS ) ]
+    --[ IsTrue( z ), IsTrue( z.1 ) ]->
+     [ C( ts, cert, status ) ]
+    variants (modulo AC)
+    1. cert  = cert.9
+       pkRS  = pkRS.9
+       resp_sig
+             = resp_sig.9
+       server_sig
+             = server_sig.9
+       status
+             = status.9
+       ts    = ts.9
+       z     = verify(resp_sig.9, <pkRS.9, cert.9, status.9, ts.9>, pkRS.9)
+       z.1   = verify(server_sig.9, <pkRS.9, cert.9, status.9, ts.9>,
+                      extract(cert.9))
+    
+    2. cert  = x.9
+       pkRS  = pk(sk(x.10))
+       resp_sig
+             = sig(<pk(sk(x.10)), x.9, x.11, x.12>, sk(x.10))
+       server_sig
+             = server_sig.13
+       status
+             = x.11
+       ts    = x.12
+       z     = true
+       z.1   = verify(server_sig.13, <pk(sk(x.10)), x.9, x.11, x.12>,
+                      extract(x.9))
+    
+    3. cert  = sig(x.9, sk(x.10))
+       pkRS  = pkRS.11
+       resp_sig
+             = resp_sig.11
+       server_sig
+             = server_sig.11
+       status
+             = status.11
+       ts    = ts.11
+       z     = verify(resp_sig.11,
+                      <pkRS.11, sig(x.9, sk(x.10)), status.11, ts.11>, pkRS.11)
+       z.1   = verify(server_sig.11,
+                      <pkRS.11, sig(x.9, sk(x.10)), status.11, ts.11>, x.9)
+    
+    4. cert  = sig(x.9, sk(x.10))
+       pkRS  = pk(sk(x.11))
+       resp_sig
+             = sig(<pk(sk(x.11)), sig(x.9, sk(x.10)), x.12, x.13>, sk(x.11))
+       server_sig
+             = server_sig.14
+       status
+             = x.12
+       ts    = x.13
+       z     = true
+       z.1   = verify(server_sig.14,
+                      <pk(sk(x.11)), sig(x.9, sk(x.10)), x.12, x.13>, x.9)
+    
+    5. cert  = sig(pk(sk(x.9)), sk(x.10))
+       pkRS  = x.11
+       resp_sig
+             = resp_sig.15
+       server_sig
+             = sig(<x.11, sig(pk(sk(x.9)), sk(x.10)), x.13, x.14>, sk(x.9))
+       status
+             = x.13
+       ts    = x.14
+       z     = verify(resp_sig.15,
+                      <x.11, sig(pk(sk(x.9)), sk(x.10)), x.13, x.14>, x.11)
+       z.1   = true
+    
+    6. cert  = sig(pk(sk(x.9)), sk(x.10))
+       pkRS  = pk(sk(x.11))
+       resp_sig
+             = sig(<pk(sk(x.11)), sig(pk(sk(x.9)), sk(x.10)), x.12, x.13>, sk(x.11))
+       server_sig
+             = sig(<pk(sk(x.11)), sig(pk(sk(x.9)), sk(x.10)), x.12, x.13>, sk(x.9))
+       status
+             = x.12
+       ts    = x.13
+       z     = true
+       z.1   = true
+  */
+
+rule (modulo E) C_judge_good:
+   [ C( ts, cert, 'good' ) ] --[ Judged( ts, cert ) ]-> [ ]
+
+  /* has exactly the trivial AC variant */
+
+rule (modulo E) C_judge_revoked:
+   [ C( ts, cert, 'revoked' ) ]
+  --[ Blame( id(extract(cert)) ), Judged( ts, cert ) ]->
+   [ ]
+
+  /*
+  rule (modulo AC) C_judge_revoked:
+     [ C( ts, cert, 'revoked' ) ] --[ Blame( z ), Judged( ts, cert ) ]-> [ ]
+    variants (modulo AC)
+    1. cert  = cert.6
+       z     = id(extract(cert.6))
+    
+    2. cert  = sig(x.7, sk(x.8))
+       z     = id(x.7)
+    
+    3. cert  = sig(pk(sk(z.7)), sk(x.9))
+       z     = z.7
+  */
+
+rule (modulo E) S_init:
+   [ !CAsk( skCA ) ]
+  --[ Server( $s ), Secret( sig(pk(sk($s)), skCA), sk($s) ) ]->
+   [
+   CertStatus( $s, sig(pk(sk($s)), skCA), 'good' ), Out( pk(sk($s)) ),
+   Out( sig(pk(sk($s)), skCA) ), !S( $s, sig(pk(sk($s)), skCA) )
+   ]
+
+  /* has exactly the trivial AC variant */
+
+rule (modulo E) S_honest:
+   [
+   In( <<pkRS, cert, status, t>, resp_sig> ), !S( $s, cert ), !RSpk( pkRS )
+   ]
+  --[ IsTrue( verify(resp_sig, <pkRS, cert, status, t>, pkRS) ) ]->
+   [
+   Out( <<pkRS, cert, status, t>, resp_sig, 
+         sig(<pkRS, cert, status, t>, sk($s))>
+   )
+   ]
+
+  /*
+  rule (modulo AC) S_honest:
+     [
+     In( <<pkRS, cert, status, t>, resp_sig> ), !S( $s, cert ), !RSpk( pkRS )
+     ]
+    --[ IsTrue( z ) ]->
+     [
+     Out( <<pkRS, cert, status, t>, resp_sig, 
+           sig(<pkRS, cert, status, t>, sk($s))>
+     )
+     ]
+    variants (modulo AC)
+    1. cert  = cert.8
+       pkRS  = pkRS.8
+       resp_sig
+             = resp_sig.8
+       status
+             = status.8
+       t     = t.8
+       z     = verify(resp_sig.8, <pkRS.8, cert.8, status.8, t.8>, pkRS.8)
+    
+    2. cert  = x.8
+       pkRS  = pk(sk(x.9))
+       resp_sig
+             = sig(<pk(sk(x.9)), x.8, x.10, x.11>, sk(x.9))
+       status
+             = x.10
+       t     = x.11
+       z     = true
+  */
+
+rule (modulo E) S_corrupt:
+   [ CertStatus( $s, cert, 'good' ) ]
+  --[ Corrupted( $s ), Time( $tn ), NewTime( $tn ), Revealed( sk($s) ) ]->
+   [ CertStatus( $s, cert, 'revoked' ), Out( sk($s) ) ]
+
+  /* has exactly the trivial AC variant */
+
+rule (modulo E) RS_corrupt:
+   [ !RS( $rs, skRS, pkCS ) ] --[ Corrupted( $rs ) ]-> [ Out( skRS ) ]
+
+  /* has exactly the trivial AC variant */
+
+restriction isTrue:
+  "∀ #i t. (IsTrue( t ) @ #i) ⇒ (t = true)"
+  // safety formula
+
+restriction clockGuideTime:
+  "∀ ts #t1 #t3.
+    (((Time( ts ) @ #t1) ∧ (Time( ts ) @ #t3)) ∧ (#t1 < #t3)) ⇒
+    (∀ ts2 #t2.
+      (((Time( ts2 ) @ #t2) ∧ (#t1 < #t2)) ∧ (#t2 < #t3)) ⇒ (ts2 = ts))"
+  // safety formula
+
+restriction NewTime:
+  "∀ ts #i #j.
+    ((NewTime( ts ) @ #i) ∧ (Time( ts ) @ #j)) ⇒ ((#i < #j) ∨ (#i = #j))"
+  // safety formula
+
+restriction CA_single_registration:
+  "∀ c cp skS #i #j.
+    ((Secret( c, skS ) @ #i) ∧ (Secret( cp, skS ) @ #j)) ⇒ (#i = #j)"
+  // safety formula
+
+restriction RS_trusted:
+  "¬(∃ x #i #j. (Corrupted( x ) @ #i) ∧ (Responder( x ) @ #j))"
+  // safety formula
+
+restriction one_role:
+  "¬(∃ x #i #j. (Responder( x ) @ #i) ∧ (Server( x ) @ #j))"
+  // safety formula
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+lemma acc_blamed_suff:
+  exists-trace
+  "∃ x #i.
+    ((Blame( x ) @ #i) ∧ (∀ x.1 #i.1. (Blame( x.1 ) @ #i.1) ⇒ (x.1 = x))) ∧
+    (∀ a #i.1. (Corrupted( a ) @ #i.1) ⇒ (a = x))"
+/*
+guarded formula characterizing all satisfying traces:
+"∃ x #i.
+  (Blame( x ) @ #i)
+ ∧
+  (∀ x.1 #i.1. (Blame( x.1 ) @ #i.1) ⇒ x.1 = x) ∧
+  (∀ a #i.1. (Corrupted( a ) @ #i.1) ⇒ a = x)"
+*/
+simplify
+solve( C( ts, cert, 'revoked' ) ▶₀ #i )
+  case C_receive
+  solve( !KU( sig(pk(sk(x)), sk(x.1)) ) @ #vk.4 )
+    case S_init
+    solve( !KU( sig(<pk(sk($rs)), sig(pk(sk($s)), sk($ca)), 'revoked', ts>,
+                    sk($rs))
+           ) @ #vk.9 )
+      case RS_resp
+      solve( !KU( sig(<pk(sk($rs)), sig(pk(sk($s)), sk($ca)), 'revoked', $tn>,
+                      sk($s))
+             ) @ #vk.10 )
+        case S_honest
+        solve( !KU( pk(sk($rs)) ) @ #vk.8 )
+          case Init
+          SOLVED // trace found
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma acc_verif_empty:
+  all-traces
+  "(¬(∃ x #i. Blame( x ) @ #i)) ⇒
+   (¬(∃ c sk t #i #j #k #l.
+       ((((Judged( t, c ) @ #i) ∧ (Secret( c, sk ) @ #j)) ∧
+         (Revealed( sk ) @ #k)) ∧
+        (Time( t ) @ #l)) ∧
+       (#k < #l)))"
+/*
+guarded formula characterizing all counter-examples:
+"(∀ x #i. (Blame( x ) @ #i) ⇒ ⊥) ∧
+ (∃ c sk t #i #j #k #l.
+   (Judged( t, c ) @ #i) ∧
+   (Secret( c, sk ) @ #j) ∧
+   (Revealed( sk ) @ #k) ∧
+   (Time( t ) @ #l)
+  ∧
+   #k < #l)"
+*/
+simplify
+solve( !CAsk( skCA ) ▶₀ #j )
+  case Init
+  solve( CertStatus( $s, cert, 'good' ) ▶₀ #k )
+    case S_init
+    solve( Judged( t, sig(pk(sk($s)), sk($ca)) ) @ #i )
+      case C_judge_good
+      solve( C( t, sig(pk(sk($s)), sk($ca)), 'good' ) ▶₀ #i )
+        case C_receive
+        solve( Time( t ) @ #l )
+          case RS_resp
+          solve( !RS( $rs, skRS, pk(sk(x)) ) ▶₀ #l )
+            case Init
+            solve( CertStatus( $s.1, sig(x, sk($ca.1)), status ) ▶₂ #l )
+              case S_corrupt
+              solve( !KU( sig(<pk(sk($rs.1)), sig(pk(sk($s)), sk($ca)), 'good', $tn>,
+                              sk($rs.1))
+                     ) @ #vk.9 )
+                case S_honest
+                by contradiction /* cyclic */
+              next
+                case c_sig
+                solve( !KU( sk($rs.1) ) @ #vk.12 )
+                  case S_corrupt
+                  by contradiction /* from formulas */
+                qed
+              qed
+            next
+              case S_init
+              solve( !KU( sig(<pk(sk($rs.1)), sig(pk(sk($s)), sk($ca)), 'good', $tn>,
+                              sk($rs.1))
+                     ) @ #vk.9 )
+                case S_honest
+                by contradiction /* cyclic */
+              next
+                case c_sig
+                solve( !KU( sk($rs.1) ) @ #vk.12 )
+                  case S_corrupt
+                  by contradiction /* from formulas */
+                qed
+              qed
+            qed
+          qed
+        next
+          case S_corrupt
+          solve( CertStatus( $s.1, cert, 'good' ) ▶₀ #l )
+            case S_init
+            solve( !KU( sig(<pk(sk($rs)), sig(pk(sk($s)), sk($ca)), 'good', $tn>,
+                            sk($rs))
+                   ) @ #vk.9 )
+              case S_honest
+              by contradiction /* cyclic */
+            next
+              case c_sig
+              solve( !KU( sk($rs) ) @ #vk.11 )
+                case S_corrupt
+                by contradiction /* from formulas */
+              qed
+            qed
+          qed
+        qed
+      qed
+    next
+      case C_judge_revoked
+      by contradiction /* from formulas */
+    qed
+  qed
+qed
+
+lemma acc_blamed_verif_nonempty:
+  all-traces
+  "∀ x #i.
+    (Blame( x ) @ #i) ⇒
+    (¬(¬(∃ c sk t #i.1 #j #k #l.
+          ((((Judged( t, c ) @ #i.1) ∧ (Secret( c, sk ) @ #j)) ∧
+            (Revealed( sk ) @ #k)) ∧
+           (Time( t ) @ #l)) ∧
+          (#k < #l))))"
+/*
+guarded formula characterizing all counter-examples:
+"∃ x #i.
+  (Blame( x ) @ #i)
+ ∧
+  ∀ c sk t #i.1 #j #k #l.
+   (Judged( t, c ) @ #i.1) ∧
+   (Secret( c, sk ) @ #j) ∧
+   (Revealed( sk ) @ #k) ∧
+   (Time( t ) @ #l)
+  ⇒
+   ¬(#k < #l)"
+*/
+simplify
+solve( C( ts, cert, 'revoked' ) ▶₀ #i )
+  case C_receive
+  solve( !KU( sig(pk(sk(x)), sk(x.1)) ) @ #vk.4 )
+    case S_init
+    solve( !KU( sig(<pk(sk($rs)), sig(pk(sk($s)), sk($ca)), 'revoked', ts>,
+                    sk($rs))
+           ) @ #vk.9 )
+      case RS_resp
+      by contradiction /* from formulas */
+    next
+      case S_honest
+      by contradiction /* cyclic */
+    next
+      case c_sig
+      solve( !KU( sk($rs) ) @ #vk.11 )
+        case S_corrupt
+        by contradiction /* from formulas */
+      qed
+    qed
+  next
+    case c_sig
+    solve( !KU( sk(x.1) ) @ #vk.12 )
+      case S_corrupt
+      solve( !KU( sig(<pk(sk($rs)), sig(pk(sk(x)), sk($s)), 'revoked', ts>,
+                      sk($rs))
+             ) @ #vk.10 )
+        case RS_resp
+        by contradiction /* from formulas */
+      next
+        case S_honest
+        by contradiction /* cyclic */
+      next
+        case c_sig
+        solve( !KU( sk($rs) ) @ #vk.13 )
+          case S_corrupt
+          by contradiction /* from formulas */
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma acc_blamed_min:
+  all-traces
+  "∀ x #i.
+    (Blame( x ) @ #i) ⇒
+    (¬(∃ x.1 #i.1. (Blame( x.1 ) @ #i.1) ∧ ((x.1 = x) ∧ (¬(x = x.1)))))"
+/*
+guarded formula characterizing all counter-examples:
+"∃ x #i.
+  (Blame( x ) @ #i)
+ ∧
+  ∃ x.1 #i.1. (Blame( x.1 ) @ #i.1) ∧ (x.1 = x) ∧ ¬(x = x.1)"
+*/
+simplify
+by contradiction /* from formulas */
+
+lemma acc_blamed_uniq:
+  all-traces "∀ x #i. (Blame( x ) @ #i) ⇒ (∃ #i.1. Corrupted( x ) @ #i.1)"
+/*
+guarded formula characterizing all counter-examples:
+"∃ x #i. (Blame( x ) @ #i) ∧ ∀ #i.1. (Corrupted( x ) @ #i.1) ⇒ ⊥"
+*/
+simplify
+solve( C( ts, cert, 'revoked' ) ▶₀ #i )
+  case C_receive
+  solve( !KU( sig(pk(sk(x)), sk(x.1)) ) @ #vk.4 )
+    case S_init
+    solve( !KU( sig(<pk(sk($rs)), sig(pk(sk($s)), sk($ca)), 'revoked', ts>,
+                    sk($rs))
+           ) @ #vk.9 )
+      case RS_resp
+      by contradiction /* from formulas */
+    next
+      case S_honest
+      by contradiction /* cyclic */
+    next
+      case c_sig
+      solve( !KU( sk($rs) ) @ #vk.11 )
+        case S_corrupt
+        by contradiction /* from formulas */
+      qed
+    qed
+  next
+    case c_sig
+    solve( !KU( sk(x.1) ) @ #vk.12 )
+      case S_corrupt
+      solve( !KU( sig(<pk(sk($rs)), sig(pk(sk(x)), sk($s)), 'revoked', ts>,
+                      sk($rs))
+             ) @ #vk.10 )
+        case RS_resp
+        by contradiction /* from formulas */
+      next
+        case S_honest
+        by contradiction /* cyclic */
+      next
+        case c_sig
+        solve( !KU( sk($rs) ) @ #vk.13 )
+          case S_corrupt
+          by contradiction /* from formulas */
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma acc_blamed_inj:
+  all-traces "⊤"
+/*
+guarded formula characterizing all counter-examples:
+"⊥"
+*/
+by contradiction /* from formulas */
+
+lemma acc_blamed_single:
+  exists-trace
+  "∃ x #i.
+    (Blame( x ) @ #i) ∧ (∀ x.1 #i.1. (Blame( x.1 ) @ #i.1) ⇒ (x.1 = x))"
+/*
+guarded formula characterizing all satisfying traces:
+"∃ x #i. (Blame( x ) @ #i) ∧ ∀ x.1 #i.1. (Blame( x.1 ) @ #i.1) ⇒ x.1 = x"
+*/
+simplify
+solve( C( ts, cert, 'revoked' ) ▶₀ #i )
+  case C_receive
+  solve( !KU( sig(pk(sk(x)), sk(x.1)) ) @ #vk.4 )
+    case S_init
+    solve( !KU( sig(<pk(sk($rs)), sig(pk(sk($s)), sk($ca)), 'revoked', ts>,
+                    sk($rs))
+           ) @ #vk.9 )
+      case RS_resp
+      solve( !KU( sig(<pk(sk($rs)), sig(pk(sk($s)), sk($ca)), 'revoked', $tn>,
+                      sk($s))
+             ) @ #vk.10 )
+        case S_honest
+        solve( !KU( pk(sk($rs)) ) @ #vk.8 )
+          case Init
+          SOLVED // trace found
+        qed
+      qed
+    qed
+  qed
+qed
+
+predicate: blamed( x )<=>∃ #i. Blame( x ) @ #i
+
+/*
+WARNING: the following wellformedness checks failed!
+
+Accountability (RP check)
+  The specification contains at least one restriction.
+  The specification contains public names.
+  At least one case test can be instantiated with non-public names.
+  
+  Please verify manually that your protocol fulfills the following condition:
+  
+  For each case test τ, traces t, t’, and instantiations ρ, ρ’:
+  If τ holds on t with ρ, and τ single-matches with ρ’ on t’, then
+  there exists a trace t’’ such that τ single-matches with ρ on t’’
+  and the parties corrupted in t’’ are the same as the parties
+  corrupted in t’ renamed from rng(ρ’) to rng(ρ).
+*/
+
+/*
+Generated from:
+Tamarin version 1.9.0
+Maude version 3.2.2
+Git revision: c838686f5a3d41b6a355eafd32cc2104ca41809c (with uncommited changes), branch: HEAD
+Compiled at: 2023-10-25 11:27:38.363683988 UTC
+*/
+
+end
+/* Output
+
+==============================================================================
+summary of summaries:
+
+analyzed: examples/accountability/csf21-acc-unbounded/previous/ocsps-msr.spthy
+
+  output:          examples/accountability/csf21-acc-unbounded/previous/ocsps-msr.spthy.tmp
+  processing time: 1.36s
+  
+  WARNING: 1 wellformedness check failed!
+           The analysis results might be wrong!
+  
+  acc_blamed_suff (exists-trace): verified (7 steps)
+  acc_verif_empty (all-traces): verified (22 steps)
+  acc_blamed_verif_nonempty (all-traces): verified (14 steps)
+  acc_blamed_min (all-traces): verified (2 steps)
+  acc_blamed_uniq (all-traces): verified (14 steps)
+  acc_blamed_inj (all-traces): verified (1 steps)
+  acc_blamed_single (exists-trace): verified (7 steps)
+
+==============================================================================
+*/
diff --git a/case-studies-regression/accountability/csf21-acc-unbounded/previous/whodunit_analyzed.spthy b/case-studies-regression/accountability/csf21-acc-unbounded/previous/whodunit_analyzed.spthy
new file mode 100644
index 000000000..6dcd4a08f
--- /dev/null
+++ b/case-studies-regression/accountability/csf21-acc-unbounded/previous/whodunit_analyzed.spthy
@@ -0,0 +1,37266 @@
+theory WhoDunit begin
+
+// Function signature and definition of the equational theory E
+
+functions: extract/1, fst/1, pair/2, pk/1, sig/2,
+           sk/1[private,destructor], snd/1, true/0, verify/3
+equations:
+    extract(sig(m, sk(i))) = m,
+    fst(<x.1, x.2>) = x.1,
+    snd(<x.1, x.2>) = x.2,
+    verify(sig(m, sk(i)), m, pk(sk(i))) = true
+
+
+
+heuristic: p
+
+
+
+
+
+
+
+
+
+
+
+
+
+restriction unequal_blame:
+  "∀ sid #i. (Unequal( sid ) @ #i) ⇒ (∃ x #j. Blame( sid, x ) @ #j)"
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+rule (modulo E) Init[color=#ffffff, process="!"]:
+   [ ] --[ Init( ) ]-> [ !Semistate_1( ) ]
+
+  /* has exactly the trivial AC variant */
+
+rule (modulo E) p_1_[color=#ffffff, process="!"]:
+   [
+   !Semistate_1( ), Fr( sid.1 ), Fr( c_SA.1 ), Fr( c_AJ.1 ), Fr( c_SJ.1 ),
+   In( <$x.1, $y.1> )
+   ]
+  -->
+   [ State_1111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ) ]
+
+  /*
+  rule (modulo AC) p_1_[color=#ffffff, process="!"]:
+     [
+     !Semistate_1( ), Fr( sid ), Fr( c_SA ), Fr( c_AJ ), Fr( c_SJ ),
+     In( <$x, $y> )
+     ]
+    -->
+     [ State_1111111( $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+  */
+
+rule (modulo E) ifxy_0_1111111[color=#408051, process="if $x.1=$y.1"]:
+   [ State_1111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ) ]
+  --[ Pred_Eq( $x.1, $y.1 ) ]->
+   [ ]
+
+  /*
+  rule (modulo AC) ifxy_0_1111111[color=#408051, process="if $x.1=$y.1"]:
+     [ State_1111111( $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+    --[ Pred_Eq( $x, $y ) ]->
+     [ ]
+  */
+
+rule (modulo E) ifxy_1_1111111[color=#408051, process="if $x.1=$y.1"]:
+   [ State_1111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ) ]
+  --[ Pred_Not_Eq( $x.1, $y.1 ) ]->
+   [
+   State_111111121( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ),
+   Out( pk(sk($x.1)) )
+   ]
+
+  /*
+  rule (modulo AC) ifxy_1_1111111[color=#408051, process="if $x.1=$y.1"]:
+     [ State_1111111( $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+    --[ Pred_Not_Eq( $x, $y ) ]->
+     [ State_111111121( $x, $y, c_AJ, c_SA, c_SJ, sid ), Out( pk(sk($x)) ) ]
+  */
+
+rule (modulo E) inv_0_11111112111111[color=#408051, process="in(v.1);"]:
+   [
+   State_11111112111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ),
+   In( v.1 )
+   ]
+  -->
+   [ State_111111121111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1, v.1 )
+   ]
+
+  /*
+  rule (modulo AC) inv_0_11111112111111[color=#408051, process="in(v.1);"]:
+     [ State_11111112111111( $x, $y, c_AJ, c_SA, c_SJ, sid ), In( v ) ]
+    -->
+     [ State_111111121111111( $x, $y, c_AJ, c_SA, c_SJ, sid, v ) ]
+  */
+
+rule (modulo E) outcSAsidvsigsidvskx_1_111111121111111[color=#408051,
+                                                       process="out(c_SA.1,<<sid.1, v.1>, sig(<sid.1, v.1>, sk($x.1))>);"]:
+   [ State_111111121111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1, v.1 )
+   ]
+  -->
+   [
+   Message( c_SA.1, <<sid.1, v.1>, sig(<sid.1, v.1>, sk($x.1))> ),
+   Semistate_1111111211111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                               v.1
+   )
+   ]
+
+  /*
+  rule (modulo AC) outcSAsidvsigsidvskx_1_111111121111111[color=#408051,
+                                                          process="out(c_SA.1,<<sid.1, v.1>, sig(<sid.1, v.1>, sk($x.1))>);"]:
+     [ State_111111121111111( $x, $y, c_AJ, c_SA, c_SJ, sid, v ) ]
+    -->
+     [
+     Message( c_SA, <<sid, v>, sig(<sid, v>, sk($x))> ),
+     Semistate_1111111211111111( $x, $y, c_AJ, c_SA, c_SJ, sid, v )
+     ]
+  */
+
+rule (modulo E) outcSAsidvsigsidvskx_0_111111121111111[color=#408051,
+                                                       process="out(c_SA.1,<<sid.1, v.1>, sig(<sid.1, v.1>, sk($x.1))>);"]:
+   [
+   State_111111121111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1, v.1 ),
+   In( c_SA.1 )
+   ]
+  -->
+   [
+   Out( <<sid.1, v.1>, sig(<sid.1, v.1>, sk($x.1))> ),
+   State_1111111211111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1, v.1 )
+   ]
+
+  /*
+  rule (modulo AC) outcSAsidvsigsidvskx_0_111111121111111[color=#408051,
+                                                          process="out(c_SA.1,<<sid.1, v.1>, sig(<sid.1, v.1>, sk($x.1))>);"]:
+     [ State_111111121111111( $x, $y, c_AJ, c_SA, c_SJ, sid, v ), In( c_SA ) ]
+    -->
+     [
+     Out( <<sid, v>, sig(<sid, v>, sk($x))> ),
+     State_1111111211111111( $x, $y, c_AJ, c_SA, c_SJ, sid, v )
+     ]
+  */
+
+rule (modulo E) outcSAsidvsigsidvskx_2_111111121111111[color=#408051,
+                                                       process="out(c_SA.1,<<sid.1, v.1>, sig(<sid.1, v.1>, sk($x.1))>);"]:
+   [
+   Semistate_1111111211111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                               v.1
+   ),
+   Ack( c_SA.1, <<sid.1, v.1>, sig(<sid.1, v.1>, sk($x.1))> )
+   ]
+  -->
+   [
+   State_1111111211111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1, v.1 )
+   ]
+
+  // loop breaker: [1]
+  /*
+  rule (modulo AC) outcSAsidvsigsidvskx_2_111111121111111[color=#408051,
+                                                          process="out(c_SA.1,<<sid.1, v.1>, sig(<sid.1, v.1>, sk($x.1))>);"]:
+     [
+     Semistate_1111111211111111( $x, $y, c_AJ, c_SA, c_SJ, sid, v ),
+     Ack( c_SA, <<sid, v>, sig(<sid, v>, sk($x))> )
+     ]
+    -->
+     [ State_1111111211111111( $x, $y, c_AJ, c_SA, c_SJ, sid, v ) ]
+    // loop breaker: [1]
+  */
+
+rule (modulo E) outcSJsidvsigsidvskx_1_1111111211111111[color=#408051,
+                                                        process="out(c_SJ.1,<<sid.1, v.1>, sig(<sid.1, v.1>, sk($x.1))>);"]:
+   [
+   State_1111111211111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1, v.1 )
+   ]
+  -->
+   [
+   Message( c_SJ.1, <<sid.1, v.1>, sig(<sid.1, v.1>, sk($x.1))> ),
+   Semistate_11111112111111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                                v.1
+   )
+   ]
+
+  /*
+  rule (modulo AC) outcSJsidvsigsidvskx_1_1111111211111111[color=#408051,
+                                                           process="out(c_SJ.1,<<sid.1, v.1>, sig(<sid.1, v.1>, sk($x.1))>);"]:
+     [ State_1111111211111111( $x, $y, c_AJ, c_SA, c_SJ, sid, v ) ]
+    -->
+     [
+     Message( c_SJ, <<sid, v>, sig(<sid, v>, sk($x))> ),
+     Semistate_11111112111111111( $x, $y, c_AJ, c_SA, c_SJ, sid, v )
+     ]
+  */
+
+rule (modulo E) outcSJsidvsigsidvskx_0_1111111211111111[color=#408051,
+                                                        process="out(c_SJ.1,<<sid.1, v.1>, sig(<sid.1, v.1>, sk($x.1))>);"]:
+   [
+   State_1111111211111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1, v.1 ),
+   In( c_SJ.1 )
+   ]
+  -->
+   [
+   Out( <<sid.1, v.1>, sig(<sid.1, v.1>, sk($x.1))> ),
+   State_11111112111111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1, v.1 )
+   ]
+
+  /*
+  rule (modulo AC) outcSJsidvsigsidvskx_0_1111111211111111[color=#408051,
+                                                           process="out(c_SJ.1,<<sid.1, v.1>, sig(<sid.1, v.1>, sk($x.1))>);"]:
+     [ State_1111111211111111( $x, $y, c_AJ, c_SA, c_SJ, sid, v ), In( c_SJ )
+     ]
+    -->
+     [
+     Out( <<sid, v>, sig(<sid, v>, sk($x))> ),
+     State_11111112111111111( $x, $y, c_AJ, c_SA, c_SJ, sid, v )
+     ]
+  */
+
+rule (modulo E) outcSJsidvsigsidvskx_2_1111111211111111[color=#408051,
+                                                        process="out(c_SJ.1,<<sid.1, v.1>, sig(<sid.1, v.1>, sk($x.1))>);"]:
+   [
+   Semistate_11111112111111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                                v.1
+   ),
+   Ack( c_SJ.1, <<sid.1, v.1>, sig(<sid.1, v.1>, sk($x.1))> )
+   ]
+  -->
+   [
+   State_11111112111111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1, v.1 )
+   ]
+
+  /*
+  rule (modulo AC) outcSJsidvsigsidvskx_2_1111111211111111[color=#408051,
+                                                           process="out(c_SJ.1,<<sid.1, v.1>, sig(<sid.1, v.1>, sk($x.1))>);"]:
+     [
+     Semistate_11111112111111111( $x, $y, c_AJ, c_SA, c_SJ, sid, v ),
+     Ack( c_SJ, <<sid, v>, sig(<sid, v>, sk($x))> )
+     ]
+    -->
+     [ State_11111112111111111( $x, $y, c_AJ, c_SA, c_SJ, sid, v ) ]
+  */
+
+rule (modulo E) incSAsidsvsigs_0_11111112111121[color=#40804a,
+                                                process="in(c_SA.1,<<sid_s.1, v.2>, sig_s.1>);"]:
+   [
+   State_11111112111121( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ),
+   Message( c_SA.1, x.2 )
+   ]
+  -->
+   [
+   Let_111111121111211( x.2, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ),
+   Ack( c_SA.1, x.2 )
+   ]
+
+  /*
+  rule (modulo AC) incSAsidsvsigs_0_11111112111121[color=#40804a,
+                                                   process="in(c_SA.1,<<sid_s.1, v.2>, sig_s.1>);"]:
+     [
+     State_11111112111121( $x, $y, c_AJ, c_SA, c_SJ, sid ),
+     Message( c_SA, x.1 )
+     ]
+    -->
+     [
+     Let_111111121111211( x.1, $x, $y, c_AJ, c_SA, c_SJ, sid ),
+     Ack( c_SA, x.1 )
+     ]
+  */
+
+rule (modulo E) incSAsidsvsigs_2_11111112111121[color=#40804a,
+                                                process="in(c_SA.1,<<sid_s.1, v.2>, sig_s.1>);"]:
+   [
+   State_11111112111121( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ),
+   In( <c_SA.1, x.2> )
+   ]
+  -->
+   [ Let_111111121111211( x.2, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ) ]
+
+  /*
+  rule (modulo AC) incSAsidsvsigs_2_11111112111121[color=#40804a,
+                                                   process="in(c_SA.1,<<sid_s.1, v.2>, sig_s.1>);"]:
+     [
+     State_11111112111121( $x, $y, c_AJ, c_SA, c_SJ, sid ), In( <c_SA, x.1> )
+     ]
+    -->
+     [ Let_111111121111211( x.1, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+  */
+
+rule (modulo E) incSAsidsvsigs_1_11111112111121[color=#40804a,
+                                                process="in(c_SA.1,<<sid_s.1, v.2>, sig_s.1>);"]:
+   [
+   Let_111111121111211( <<sid_s.1, v.2>, sig_s.1>, $x.1, $y.1, c_AJ.1,
+                        c_SA.1, c_SJ.1, sid.1
+   )
+   ]
+  -->
+   [
+   State_111111121111211( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                          sid_s.1, sig_s.1, v.2
+   )
+   ]
+
+  // loop breaker: [0]
+  /*
+  rule (modulo AC) incSAsidsvsigs_1_11111112111121[color=#40804a,
+                                                   process="in(c_SA.1,<<sid_s.1, v.2>, sig_s.1>);"]:
+     [
+     Let_111111121111211( <<sid_s, v>, sig_s>, $x, $y, c_AJ, c_SA, c_SJ, sid )
+     ]
+    -->
+     [ State_111111121111211( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_s, sig_s, v )
+     ]
+    // loop breaker: [0]
+  */
+
+rule (modulo E) incSAsidsvsigs_3_11111112111121[color=#40804a,
+                                                process="in(c_SA.1,<<sid_s.1, v.2>, sig_s.1>);"]:
+   [
+   Let_111111121111211( <<sid_s.1, v.2>, sig_s.1>, $x.1, $y.1, c_AJ.1,
+                        c_SA.1, c_SJ.1, sid.1
+   )
+   ]
+  -->
+   [
+   State_111111121111211( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                          sid_s.1, sig_s.1, v.2
+   )
+   ]
+
+  // loop breaker: [0]
+  /*
+  rule (modulo AC) incSAsidsvsigs_3_11111112111121[color=#40804a,
+                                                   process="in(c_SA.1,<<sid_s.1, v.2>, sig_s.1>);"]:
+     [
+     Let_111111121111211( <<sid_s, v>, sig_s>, $x, $y, c_AJ, c_SA, c_SJ, sid )
+     ]
+    -->
+     [ State_111111121111211( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_s, sig_s, v )
+     ]
+    // loop breaker: [0]
+  */
+
+rule (modulo E) ifverifysigssidvpkskxtrue_0_111111121111211[color=#40804a,
+                                                            process="if verify(sig_s.1, <sid.1, v.2>, pk(sk($x.1)))=true"]:
+   [
+   State_111111121111211( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                          sid_s.1, sig_s.1, v.2
+   )
+   ]
+  --[ Pred_Eq( verify(sig_s.1, <sid.1, v.2>, pk(sk($x.1))), true ) ]->
+   [
+   State_1111111211112111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                           sid_s.1, sig_s.1, v.2
+   )
+   ]
+
+  /*
+  rule (modulo AC) ifverifysigssidvpkskxtrue_0_111111121111211[color=#40804a,
+                                                               process="if verify(sig_s.1, <sid.1, v.2>, pk(sk($x.1)))=true"]:
+     [ State_111111121111211( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_s, sig_s, v )
+     ]
+    --[ Pred_Eq( z, true ) ]->
+     [
+     State_1111111211112111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_s, sig_s, v )
+     ]
+    variants (modulo AC)
+    1. $x    = $x.13
+       sid   = sid.13
+       sig_s = sig_s.13
+       v     = v.14
+       z     = verify(sig_s.13, <sid.13, v.14>, pk(sk($x.13)))
+    
+    2. $x    = $x.13
+       sid   = x.18
+       sig_s = sig(<x.18, x.20>, sk($x.13))
+       v     = x.20
+       z     = true
+  */
+
+rule (modulo E) outcAJsidvsigssigsidvsky_1_1111111211112111[color=#40804a,
+                                                            process="out(c_AJ.1,<<sid.1, v.2>, sig_s.1, sig(<sid.1, v.2>, sk($y.1))>);"]:
+   [
+   State_1111111211112111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                           sid_s.1, sig_s.1, v.2
+   )
+   ]
+  -->
+   [
+   Message( c_AJ.1, <<sid.1, v.2>, sig_s.1, sig(<sid.1, v.2>, sk($y.1))> ),
+   Semistate_11111112111121111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                                sid_s.1, sig_s.1, v.2
+   )
+   ]
+
+  /*
+  rule (modulo AC) outcAJsidvsigssigsidvsky_1_1111111211112111[color=#40804a,
+                                                               process="out(c_AJ.1,<<sid.1, v.2>, sig_s.1, sig(<sid.1, v.2>, sk($y.1))>);"]:
+     [
+     State_1111111211112111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_s, sig_s, v )
+     ]
+    -->
+     [
+     Message( c_AJ, <<sid, v>, sig_s, sig(<sid, v>, sk($y))> ),
+     Semistate_11111112111121111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_s, sig_s,
+                                  v
+     )
+     ]
+  */
+
+rule (modulo E) outcAJsidvsigssigsidvsky_0_1111111211112111[color=#40804a,
+                                                            process="out(c_AJ.1,<<sid.1, v.2>, sig_s.1, sig(<sid.1, v.2>, sk($y.1))>);"]:
+   [
+   State_1111111211112111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                           sid_s.1, sig_s.1, v.2
+   ),
+   In( c_AJ.1 )
+   ]
+  -->
+   [
+   Out( <<sid.1, v.2>, sig_s.1, sig(<sid.1, v.2>, sk($y.1))> ),
+   State_11111112111121111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                            sid_s.1, sig_s.1, v.2
+   )
+   ]
+
+  /*
+  rule (modulo AC) outcAJsidvsigssigsidvsky_0_1111111211112111[color=#40804a,
+                                                               process="out(c_AJ.1,<<sid.1, v.2>, sig_s.1, sig(<sid.1, v.2>, sk($y.1))>);"]:
+     [
+     State_1111111211112111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_s, sig_s, v ),
+     In( c_AJ )
+     ]
+    -->
+     [
+     Out( <<sid, v>, sig_s, sig(<sid, v>, sk($y))> ),
+     State_11111112111121111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_s, sig_s, v )
+     ]
+  */
+
+rule (modulo E) outcAJsidvsigssigsidvsky_2_1111111211112111[color=#40804a,
+                                                            process="out(c_AJ.1,<<sid.1, v.2>, sig_s.1, sig(<sid.1, v.2>, sk($y.1))>);"]:
+   [
+   Semistate_11111112111121111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                                sid_s.1, sig_s.1, v.2
+   ),
+   Ack( c_AJ.1, <<sid.1, v.2>, sig_s.1, sig(<sid.1, v.2>, sk($y.1))> )
+   ]
+  -->
+   [
+   State_11111112111121111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                            sid_s.1, sig_s.1, v.2
+   )
+   ]
+
+  /*
+  rule (modulo AC) outcAJsidvsigssigsidvsky_2_1111111211112111[color=#40804a,
+                                                               process="out(c_AJ.1,<<sid.1, v.2>, sig_s.1, sig(<sid.1, v.2>, sk($y.1))>);"]:
+     [
+     Semistate_11111112111121111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_s, sig_s,
+                                  v
+     ),
+     Ack( c_AJ, <<sid, v>, sig_s, sig(<sid, v>, sk($y))> )
+     ]
+    -->
+     [
+     State_11111112111121111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_s, sig_s, v )
+     ]
+  */
+
+rule (modulo E) ifverifysigssidvpkskxtrue_1_111111121111211[color=#40804a,
+                                                            process="if verify(sig_s.1, <sid.1, v.2>, pk(sk($x.1)))=true"]:
+   [
+   State_111111121111211( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                          sid_s.1, sig_s.1, v.2
+   )
+   ]
+  --[ Pred_Not_Eq( verify(sig_s.1, <sid.1, v.2>, pk(sk($x.1))), true ) ]->
+   [ ]
+
+  /*
+  rule (modulo AC) ifverifysigssidvpkskxtrue_1_111111121111211[color=#40804a,
+                                                               process="if verify(sig_s.1, <sid.1, v.2>, pk(sk($x.1)))=true"]:
+     [ State_111111121111211( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_s, sig_s, v )
+     ]
+    --[ Pred_Not_Eq( z, true ) ]->
+     [ ]
+    variants (modulo AC)
+    1. $x    = $x.13
+       sid   = sid.13
+       sig_s = sig_s.13
+       v     = v.14
+       z     = verify(sig_s.13, <sid.13, v.14>, pk(sk($x.13)))
+    
+    2. $x    = $x.13
+       sid   = x.18
+       sig_s = sig(<x.18, x.20>, sk($x.13))
+       v     = x.20
+       z     = true
+  */
+
+rule (modulo E) incSJsidsvssigs_0_1111111211121[color=#40807d,
+                                                process="in(c_SJ.1,<<sid_s.2, v_s.1>, sig1_s.1>);"]:
+   [
+   State_1111111211121( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ),
+   Message( c_SJ.1, x.2 )
+   ]
+  -->
+   [
+   Let_11111112111211( x.2, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ),
+   Ack( c_SJ.1, x.2 )
+   ]
+
+  /*
+  rule (modulo AC) incSJsidsvssigs_0_1111111211121[color=#40807d,
+                                                   process="in(c_SJ.1,<<sid_s.2, v_s.1>, sig1_s.1>);"]:
+     [
+     State_1111111211121( $x, $y, c_AJ, c_SA, c_SJ, sid ),
+     Message( c_SJ, x.1 )
+     ]
+    -->
+     [
+     Let_11111112111211( x.1, $x, $y, c_AJ, c_SA, c_SJ, sid ),
+     Ack( c_SJ, x.1 )
+     ]
+  */
+
+rule (modulo E) incSJsidsvssigs_2_1111111211121[color=#40807d,
+                                                process="in(c_SJ.1,<<sid_s.2, v_s.1>, sig1_s.1>);"]:
+   [
+   State_1111111211121( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ),
+   In( <c_SJ.1, x.2> )
+   ]
+  -->
+   [ Let_11111112111211( x.2, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ) ]
+
+  /*
+  rule (modulo AC) incSJsidsvssigs_2_1111111211121[color=#40807d,
+                                                   process="in(c_SJ.1,<<sid_s.2, v_s.1>, sig1_s.1>);"]:
+     [ State_1111111211121( $x, $y, c_AJ, c_SA, c_SJ, sid ), In( <c_SJ, x.1> )
+     ]
+    -->
+     [ Let_11111112111211( x.1, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+  */
+
+rule (modulo E) incSJsidsvssigs_1_1111111211121[color=#40807d,
+                                                process="in(c_SJ.1,<<sid_s.2, v_s.1>, sig1_s.1>);"]:
+   [
+   Let_11111112111211( <<sid_s.2, v_s.1>, sig1_s.1>, $x.1, $y.1, c_AJ.1,
+                       c_SA.1, c_SJ.1, sid.1
+   )
+   ]
+  -->
+   [
+   State_11111112111211( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                         sig1_s.1, v_s.1, sid_s.2
+   )
+   ]
+
+  /*
+  rule (modulo AC) incSJsidsvssigs_1_1111111211121[color=#40807d,
+                                                   process="in(c_SJ.1,<<sid_s.2, v_s.1>, sig1_s.1>);"]:
+     [
+     Let_11111112111211( <<sid_s, v_s>, sig1_s>, $x, $y, c_AJ, c_SA, c_SJ, sid
+     )
+     ]
+    -->
+     [
+     State_11111112111211( $x, $y, c_AJ, c_SA, c_SJ, sid, sig1_s, v_s, sid_s )
+     ]
+  */
+
+rule (modulo E) incSJsidsvssigs_3_1111111211121[color=#40807d,
+                                                process="in(c_SJ.1,<<sid_s.2, v_s.1>, sig1_s.1>);"]:
+   [
+   Let_11111112111211( <<sid_s.2, v_s.1>, sig1_s.1>, $x.1, $y.1, c_AJ.1,
+                       c_SA.1, c_SJ.1, sid.1
+   )
+   ]
+  -->
+   [
+   State_11111112111211( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                         sig1_s.1, v_s.1, sid_s.2
+   )
+   ]
+
+  /*
+  rule (modulo AC) incSJsidsvssigs_3_1111111211121[color=#40807d,
+                                                   process="in(c_SJ.1,<<sid_s.2, v_s.1>, sig1_s.1>);"]:
+     [
+     Let_11111112111211( <<sid_s, v_s>, sig1_s>, $x, $y, c_AJ, c_SA, c_SJ, sid
+     )
+     ]
+    -->
+     [
+     State_11111112111211( $x, $y, c_AJ, c_SA, c_SJ, sid, sig1_s, v_s, sid_s )
+     ]
+  */
+
+rule (modulo E) incAJsidavasigssiga_0_11111112111211[color=#40807d,
+                                                     process="in(c_AJ.1,<<sid_a.1, v_a.1>, sig2_s.1, sig_a.1>);"]:
+   [
+   State_11111112111211( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                         sig1_s.1, v_s.1, sid_s.2
+   ),
+   Message( c_AJ.1, x.3 )
+   ]
+  -->
+   [
+   Let_111111121112111( x.3, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                        sig1_s.1, v_s.1, sid_s.2
+   ),
+   Ack( c_AJ.1, x.3 )
+   ]
+
+  /*
+  rule (modulo AC) incAJsidavasigssiga_0_11111112111211[color=#40807d,
+                                                        process="in(c_AJ.1,<<sid_a.1, v_a.1>, sig2_s.1, sig_a.1>);"]:
+     [
+     State_11111112111211( $x, $y, c_AJ, c_SA, c_SJ, sid, sig1_s, v_s, sid_s
+     ),
+     Message( c_AJ, x.1 )
+     ]
+    -->
+     [
+     Let_111111121112111( x.1, $x, $y, c_AJ, c_SA, c_SJ, sid, sig1_s, v_s,
+                          sid_s
+     ),
+     Ack( c_AJ, x.1 )
+     ]
+  */
+
+rule (modulo E) incAJsidavasigssiga_2_11111112111211[color=#40807d,
+                                                     process="in(c_AJ.1,<<sid_a.1, v_a.1>, sig2_s.1, sig_a.1>);"]:
+   [
+   State_11111112111211( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                         sig1_s.1, v_s.1, sid_s.2
+   ),
+   In( <c_AJ.1, x.3> )
+   ]
+  -->
+   [
+   Let_111111121112111( x.3, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                        sig1_s.1, v_s.1, sid_s.2
+   )
+   ]
+
+  /*
+  rule (modulo AC) incAJsidavasigssiga_2_11111112111211[color=#40807d,
+                                                        process="in(c_AJ.1,<<sid_a.1, v_a.1>, sig2_s.1, sig_a.1>);"]:
+     [
+     State_11111112111211( $x, $y, c_AJ, c_SA, c_SJ, sid, sig1_s, v_s, sid_s
+     ),
+     In( <c_AJ, x.1> )
+     ]
+    -->
+     [
+     Let_111111121112111( x.1, $x, $y, c_AJ, c_SA, c_SJ, sid, sig1_s, v_s,
+                          sid_s
+     )
+     ]
+  */
+
+rule (modulo E) incAJsidavasigssiga_1_11111112111211[color=#40807d,
+                                                     process="in(c_AJ.1,<<sid_a.1, v_a.1>, sig2_s.1, sig_a.1>);"]:
+   [
+   Let_111111121112111( <<sid_a.1, v_a.1>, sig2_s.1, sig_a.1>, $x.1, $y.1,
+                        c_AJ.1, c_SA.1, c_SJ.1, sid.1, sig1_s.1, v_s.1, sid_s.2
+   )
+   ]
+  -->
+   [
+   State_111111121112111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                          sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+
+  /*
+  rule (modulo AC) incAJsidavasigssiga_1_11111112111211[color=#40807d,
+                                                        process="in(c_AJ.1,<<sid_a.1, v_a.1>, sig2_s.1, sig_a.1>);"]:
+     [
+     Let_111111121112111( <<sid_a, v_a>, sig2_s, sig_a>, $x, $y, c_AJ, c_SA,
+                          c_SJ, sid, sig1_s, v_s, sid_s
+     )
+     ]
+    -->
+     [
+     State_111111121112111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                            sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+  */
+
+rule (modulo E) incAJsidavasigssiga_3_11111112111211[color=#40807d,
+                                                     process="in(c_AJ.1,<<sid_a.1, v_a.1>, sig2_s.1, sig_a.1>);"]:
+   [
+   Let_111111121112111( <<sid_a.1, v_a.1>, sig2_s.1, sig_a.1>, $x.1, $y.1,
+                        c_AJ.1, c_SA.1, c_SJ.1, sid.1, sig1_s.1, v_s.1, sid_s.2
+   )
+   ]
+  -->
+   [
+   State_111111121112111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                          sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+
+  /*
+  rule (modulo AC) incAJsidavasigssiga_3_11111112111211[color=#40807d,
+                                                        process="in(c_AJ.1,<<sid_a.1, v_a.1>, sig2_s.1, sig_a.1>);"]:
+     [
+     Let_111111121112111( <<sid_a, v_a>, sig2_s, sig_a>, $x, $y, c_AJ, c_SA,
+                          c_SJ, sid, sig1_s, v_s, sid_s
+     )
+     ]
+    -->
+     [
+     State_111111121112111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                            sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+  */
+
+rule (modulo E) ifverifysigssidvspkskxtrue_0_111111121112111[color=#40807d,
+                                                             process="if verify(sig1_s.1, <sid.1, v_s.1>, pk(sk($x.1)))=true"]:
+   [
+   State_111111121112111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                          sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+  --[ Pred_Eq( verify(sig1_s.1, <sid.1, v_s.1>, pk(sk($x.1))), true ) ]->
+   [
+   State_1111111211121111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                           sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+
+  /*
+  rule (modulo AC) ifverifysigssidvspkskxtrue_0_111111121112111[color=#40807d,
+                                                                process="if verify(sig1_s.1, <sid.1, v_s.1>, pk(sk($x.1)))=true"]:
+     [
+     State_111111121112111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                            sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+    --[ Pred_Eq( z, true ) ]->
+     [
+     State_1111111211121111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                             sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+    variants (modulo AC)
+    1. $x    = $x.17
+       sid   = sid.17
+       sig1_s
+             = sig1_s.17
+       v_s   = v_s.17
+       z     = verify(sig1_s.17, <sid.17, v_s.17>, pk(sk($x.17)))
+    
+    2. $x    = $x.17
+       sid   = x.22
+       sig1_s
+             = sig(<x.22, x.24>, sk($x.17))
+       v_s   = x.24
+       z     = true
+  */
+
+rule (modulo E) ifverifysigssidvapkskxtrue_0_1111111211121111[color=#40807d,
+                                                              process="if verify(sig2_s.1, <sid.1, v_a.1>, pk(sk($x.1)))=true"]:
+   [
+   State_1111111211121111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                           sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+  --[ Pred_Eq( verify(sig2_s.1, <sid.1, v_a.1>, pk(sk($x.1))), true ) ]->
+   [
+   State_11111112111211111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                            sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+
+  /*
+  rule (modulo AC) ifverifysigssidvapkskxtrue_0_1111111211121111[color=#40807d,
+                                                                 process="if verify(sig2_s.1, <sid.1, v_a.1>, pk(sk($x.1)))=true"]:
+     [
+     State_1111111211121111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                             sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+    --[ Pred_Eq( z, true ) ]->
+     [
+     State_11111112111211111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                              sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+    variants (modulo AC)
+    1. $x    = $x.17
+       sid   = sid.17
+       sig2_s
+             = sig2_s.17
+       v_a   = v_a.17
+       z     = verify(sig2_s.17, <sid.17, v_a.17>, pk(sk($x.17)))
+    
+    2. $x    = $x.17
+       sid   = x.22
+       sig2_s
+             = sig(<x.22, x.25>, sk($x.17))
+       v_a   = x.25
+       z     = true
+  */
+
+rule (modulo E) ifverifysigasidvapkskytrue_0_11111112111211111[color=#40807d,
+                                                               process="if verify(sig_a.1, <sid.1, v_a.1>, pk(sk($y.1)))=true"]:
+   [
+   State_11111112111211111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                            sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+  --[ Pred_Eq( verify(sig_a.1, <sid.1, v_a.1>, pk(sk($y.1))), true ) ]->
+   [
+   State_111111121112111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                             sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+
+  /*
+  rule (modulo AC) ifverifysigasidvapkskytrue_0_11111112111211111[color=#40807d,
+                                                                  process="if verify(sig_a.1, <sid.1, v_a.1>, pk(sk($y.1)))=true"]:
+     [
+     State_11111112111211111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                              sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+    --[ Pred_Eq( z, true ) ]->
+     [
+     State_111111121112111111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                               sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+    variants (modulo AC)
+    1. $y    = $x.17
+       sid   = x.21
+       sig_a = sig(<x.21, x.25>, sk($x.17))
+       v_a   = x.25
+       z     = true
+    
+    2. $y    = $y.17
+       sid   = sid.17
+       sig_a = sig_a.17
+       v_a   = v_a.17
+       z     = verify(sig_a.17, <sid.17, v_a.17>, pk(sk($y.17)))
+  */
+
+rule (modulo E) ifvsva_0_111111121112111111[color=#40807d,
+                                            process="if v_s.1=v_a.1"]:
+   [
+   State_111111121112111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                             sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+  --[ Pred_Eq( v_s.1, v_a.1 ) ]->
+   [
+   State_1111111211121111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                              sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+
+  /*
+  rule (modulo AC) ifvsva_0_111111121112111111[color=#40807d,
+                                               process="if v_s.1=v_a.1"]:
+     [
+     State_111111121112111111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                               sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+    --[ Pred_Eq( v_s, v_a ) ]->
+     [
+     State_1111111211121111111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                                sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+  */
+
+rule (modulo E) eventEqualsid_0_1111111211121111111[color=#40807d,
+                                                    process="event Equal( sid.1 );"]:
+   [
+   State_1111111211121111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                              sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+  --[ Equal( sid.1 ) ]->
+   [ ]
+
+  /*
+  rule (modulo AC) eventEqualsid_0_1111111211121111111[color=#40807d,
+                                                       process="event Equal( sid.1 );"]:
+     [
+     State_1111111211121111111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                                sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+    --[ Equal( sid ) ]->
+     [ ]
+  */
+
+rule (modulo E) ifvsva_1_111111121112111111[color=#40807d,
+                                            process="if v_s.1=v_a.1"]:
+   [
+   State_111111121112111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                             sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+  --[ Pred_Not_Eq( v_s.1, v_a.1 ) ]->
+   [
+   State_1111111211121111112( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                              sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+
+  /*
+  rule (modulo AC) ifvsva_1_111111121112111111[color=#40807d,
+                                               process="if v_s.1=v_a.1"]:
+     [
+     State_111111121112111111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                               sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+    --[ Pred_Not_Eq( v_s, v_a ) ]->
+     [
+     State_1111111211121111112( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                                sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+  */
+
+rule (modulo E) eventUnequalsid_0_1111111211121111112[color=#40807d,
+                                                      process="event Unequal( sid.1 );"]:
+   [
+   State_1111111211121111112( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                              sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+  --[ Unequal( sid.1 ) ]->
+   [
+   State_11111112111211111121( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                               sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+
+  /*
+  rule (modulo AC) eventUnequalsid_0_1111111211121111112[color=#40807d,
+                                                         process="event Unequal( sid.1 );"]:
+     [
+     State_1111111211121111112( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                                sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+    --[ Unequal( sid ) ]->
+     [
+     State_11111112111211111121( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                                 sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+  */
+
+rule (modulo E) eventBlamesidx_0_11111112111211111121[color=#40807d,
+                                                      process="event Blame( sid.1, $x.1 );"]:
+   [
+   State_11111112111211111121( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                               sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+  --[ Blame( sid.1, $x.1 ) ]->
+   [ ]
+
+  /*
+  rule (modulo AC) eventBlamesidx_0_11111112111211111121[color=#40807d,
+                                                         process="event Blame( sid.1, $x.1 );"]:
+     [
+     State_11111112111211111121( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                                 sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+    --[ Blame( sid, $x ) ]->
+     [ ]
+  */
+
+rule (modulo E) ifverifysigasidvapkskytrue_1_11111112111211111[color=#40807d,
+                                                               process="if verify(sig_a.1, <sid.1, v_a.1>, pk(sk($y.1)))=true"]:
+   [
+   State_11111112111211111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                            sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+  --[ Pred_Not_Eq( verify(sig_a.1, <sid.1, v_a.1>, pk(sk($y.1))), true )
+  ]->
+   [ ]
+
+  /*
+  rule (modulo AC) ifverifysigasidvapkskytrue_1_11111112111211111[color=#40807d,
+                                                                  process="if verify(sig_a.1, <sid.1, v_a.1>, pk(sk($y.1)))=true"]:
+     [
+     State_11111112111211111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                              sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+    --[ Pred_Not_Eq( z, true ) ]->
+     [ ]
+    variants (modulo AC)
+    1. $y    = $x.17
+       sid   = x.21
+       sig_a = sig(<x.21, x.25>, sk($x.17))
+       v_a   = x.25
+       z     = true
+    
+    2. $y    = $y.17
+       sid   = sid.17
+       sig_a = sig_a.17
+       v_a   = v_a.17
+       z     = verify(sig_a.17, <sid.17, v_a.17>, pk(sk($y.17)))
+  */
+
+rule (modulo E) ifverifysigssidvapkskxtrue_1_1111111211121111[color=#40807d,
+                                                              process="if verify(sig2_s.1, <sid.1, v_a.1>, pk(sk($x.1)))=true"]:
+   [
+   State_1111111211121111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                           sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+  --[ Pred_Not_Eq( verify(sig2_s.1, <sid.1, v_a.1>, pk(sk($x.1))), true )
+  ]->
+   [ ]
+
+  /*
+  rule (modulo AC) ifverifysigssidvapkskxtrue_1_1111111211121111[color=#40807d,
+                                                                 process="if verify(sig2_s.1, <sid.1, v_a.1>, pk(sk($x.1)))=true"]:
+     [
+     State_1111111211121111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                             sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+    --[ Pred_Not_Eq( z, true ) ]->
+     [ ]
+    variants (modulo AC)
+    1. $x    = $x.17
+       sid   = sid.17
+       sig2_s
+             = sig2_s.17
+       v_a   = v_a.17
+       z     = verify(sig2_s.17, <sid.17, v_a.17>, pk(sk($x.17)))
+    
+    2. $x    = $x.17
+       sid   = x.22
+       sig2_s
+             = sig(<x.22, x.25>, sk($x.17))
+       v_a   = x.25
+       z     = true
+  */
+
+rule (modulo E) ifverifysigssidvspkskxtrue_1_111111121112111[color=#40807d,
+                                                             process="if verify(sig1_s.1, <sid.1, v_s.1>, pk(sk($x.1)))=true"]:
+   [
+   State_111111121112111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1,
+                          sid_a.1, sig1_s.1, sig2_s.1, sig_a.1, v_a.1, v_s.1, sid_s.2
+   )
+   ]
+  --[ Pred_Not_Eq( verify(sig1_s.1, <sid.1, v_s.1>, pk(sk($x.1))), true )
+  ]->
+   [ ]
+
+  /*
+  rule (modulo AC) ifverifysigssidvspkskxtrue_1_111111121112111[color=#40807d,
+                                                                process="if verify(sig1_s.1, <sid.1, v_s.1>, pk(sk($x.1)))=true"]:
+     [
+     State_111111121112111( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a, sig1_s,
+                            sig2_s, sig_a, v_a, v_s, sid_s
+     )
+     ]
+    --[ Pred_Not_Eq( z, true ) ]->
+     [ ]
+    variants (modulo AC)
+    1. $x    = $x.17
+       sid   = sid.17
+       sig1_s
+             = sig1_s.17
+       v_s   = v_s.17
+       z     = verify(sig1_s.17, <sid.17, v_s.17>, pk(sk($x.17)))
+    
+    2. $x    = $x.17
+       sid   = x.22
+       sig1_s
+             = sig(<x.22, x.24>, sk($x.17))
+       v_s   = x.24
+       z     = true
+  */
+
+rule (modulo E) outpksky_0_111111121[color=#408051,
+                                     process="out(pk(sk($y.1)));"]:
+   [ State_111111121( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ) ]
+  -->
+   [
+   !Semistate_111111121121( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ),
+   State_1111111211121( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ),
+   State_11111112111121( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ),
+   State_11111112111111( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ),
+   Out( pk(sk($y.1)) )
+   ]
+
+  /*
+  rule (modulo AC) outpksky_0_111111121[color=#408051,
+                                        process="out(pk(sk($y.1)));"]:
+     [ State_111111121( $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+    -->
+     [
+     !Semistate_111111121121( $x, $y, c_AJ, c_SA, c_SJ, sid ),
+     State_1111111211121( $x, $y, c_AJ, c_SA, c_SJ, sid ),
+     State_11111112111121( $x, $y, c_AJ, c_SA, c_SJ, sid ),
+     State_11111112111111( $x, $y, c_AJ, c_SA, c_SJ, sid ), Out( pk(sk($y)) )
+     ]
+  */
+
+rule (modulo E) p_1_11111112112[color=#408051, process="!"]:
+   [ !Semistate_111111121121( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ) ]
+  -->
+   [ State_1111111211211( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ) ]
+
+  /*
+  rule (modulo AC) p_1_11111112112[color=#408051, process="!"]:
+     [ !Semistate_111111121121( $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+    -->
+     [ State_1111111211211( $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+  */
+
+rule (modulo E) inccorruptp_0_1111111211211[color=#408058,
+                                            process="in('c',<'corrupt', $p.1>);"]:
+   [
+   State_1111111211211( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ),
+   Message( 'c', x.2 )
+   ]
+  -->
+   [
+   Let_11111112112111( x.2, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ),
+   Ack( 'c', x.2 )
+   ]
+
+  // loop breaker: [1]
+  /*
+  rule (modulo AC) inccorruptp_0_1111111211211[color=#408058,
+                                               process="in('c',<'corrupt', $p.1>);"]:
+     [
+     State_1111111211211( $x, $y, c_AJ, c_SA, c_SJ, sid ), Message( 'c', x.1 )
+     ]
+    -->
+     [
+     Let_11111112112111( x.1, $x, $y, c_AJ, c_SA, c_SJ, sid ), Ack( 'c', x.1 )
+     ]
+    // loop breaker: [1]
+  */
+
+rule (modulo E) inccorruptp_2_1111111211211[color=#408058,
+                                            process="in('c',<'corrupt', $p.1>);"]:
+   [
+   State_1111111211211( $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ),
+   In( <'c', x.2> )
+   ]
+  -->
+   [ Let_11111112112111( x.2, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 ) ]
+
+  /*
+  rule (modulo AC) inccorruptp_2_1111111211211[color=#408058,
+                                               process="in('c',<'corrupt', $p.1>);"]:
+     [ State_1111111211211( $x, $y, c_AJ, c_SA, c_SJ, sid ), In( <'c', x.1> )
+     ]
+    -->
+     [ Let_11111112112111( x.1, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+  */
+
+rule (modulo E) inccorruptp_1_1111111211211[color=#408058,
+                                            process="in('c',<'corrupt', $p.1>);"]:
+   [
+   Let_11111112112111( <'corrupt', $p.1>, $x.1, $y.1, c_AJ.1, c_SA.1,
+                       c_SJ.1, sid.1
+   )
+   ]
+  -->
+   [ State_11111112112111( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 )
+   ]
+
+  /*
+  rule (modulo AC) inccorruptp_1_1111111211211[color=#408058,
+                                               process="in('c',<'corrupt', $p.1>);"]:
+     [ Let_11111112112111( <'corrupt', $p>, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+    -->
+     [ State_11111112112111( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+  */
+
+rule (modulo E) inccorruptp_3_1111111211211[color=#408058,
+                                            process="in('c',<'corrupt', $p.1>);"]:
+   [
+   Let_11111112112111( <'corrupt', $p.1>, $x.1, $y.1, c_AJ.1, c_SA.1,
+                       c_SJ.1, sid.1
+   )
+   ]
+  -->
+   [ State_11111112112111( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 )
+   ]
+
+  /*
+  rule (modulo AC) inccorruptp_3_1111111211211[color=#408058,
+                                               process="in('c',<'corrupt', $p.1>);"]:
+     [ Let_11111112112111( <'corrupt', $p>, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+    -->
+     [ State_11111112112111( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+  */
+
+rule (modulo E) eventCorruptedp_0_11111112112111[color=#40805f,
+                                                 process="event Corrupted( $p.1 );"]:
+   [ State_11111112112111( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 )
+   ]
+  --[ Corrupted( $p.1 ) ]->
+   [
+   State_111111121121111( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 )
+   ]
+
+  /*
+  rule (modulo AC) eventCorruptedp_0_11111112112111[color=#40805f,
+                                                    process="event Corrupted( $p.1 );"]:
+     [ State_11111112112111( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+    --[ Corrupted( $p ) ]->
+     [ State_111111121121111( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+  */
+
+rule (modulo E) ifpx_0_111111121121111[color=#40805f,
+                                       process="if $p.1=$x.1"]:
+   [
+   State_111111121121111( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 )
+   ]
+  --[ Pred_Eq( $p.1, $x.1 ) ]->
+   [
+   State_1111111211211111( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 )
+   ]
+
+  /*
+  rule (modulo AC) ifpx_0_111111121121111[color=#40805f,
+                                          process="if $p.1=$x.1"]:
+     [ State_111111121121111( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+    --[ Pred_Eq( $p, $x ) ]->
+     [ State_1111111211211111( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+  */
+
+rule (modulo E) outcskpsidcSAcSJ_1_1111111211211111[color=#40805f,
+                                                    process="out('c',<sk($p.1), sid.1, c_SA.1, c_SJ.1>);"]:
+   [
+   State_1111111211211111( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 )
+   ]
+  -->
+   [
+   Message( 'c', <sk($p.1), sid.1, c_SA.1, c_SJ.1> ),
+   Semistate_11111112112111111( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1,
+                                sid.1
+   )
+   ]
+
+  /*
+  rule (modulo AC) outcskpsidcSAcSJ_1_1111111211211111[color=#40805f,
+                                                       process="out('c',<sk($p.1), sid.1, c_SA.1, c_SJ.1>);"]:
+     [ State_1111111211211111( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+    -->
+     [
+     Message( 'c', <sk($p), sid, c_SA, c_SJ> ),
+     Semistate_11111112112111111( $p, $x, $y, c_AJ, c_SA, c_SJ, sid )
+     ]
+  */
+
+rule (modulo E) outcskpsidcSAcSJ_0_1111111211211111[color=#40805f,
+                                                    process="out('c',<sk($p.1), sid.1, c_SA.1, c_SJ.1>);"]:
+   [
+   State_1111111211211111( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1
+   ),
+   In( 'c' )
+   ]
+  -->
+   [
+   Out( <sk($p.1), sid.1, c_SA.1, c_SJ.1> ),
+   State_11111112112111111( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1
+   )
+   ]
+
+  /*
+  rule (modulo AC) outcskpsidcSAcSJ_0_1111111211211111[color=#40805f,
+                                                       process="out('c',<sk($p.1), sid.1, c_SA.1, c_SJ.1>);"]:
+     [ State_1111111211211111( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ), In( 'c' )
+     ]
+    -->
+     [
+     Out( <sk($p), sid, c_SA, c_SJ> ),
+     State_11111112112111111( $p, $x, $y, c_AJ, c_SA, c_SJ, sid )
+     ]
+  */
+
+rule (modulo E) outcskpsidcSAcSJ_2_1111111211211111[color=#40805f,
+                                                    process="out('c',<sk($p.1), sid.1, c_SA.1, c_SJ.1>);"]:
+   [
+   Semistate_11111112112111111( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1,
+                                sid.1
+   ),
+   Ack( 'c', <sk($p.1), sid.1, c_SA.1, c_SJ.1> )
+   ]
+  -->
+   [
+   State_11111112112111111( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1
+   )
+   ]
+
+  /*
+  rule (modulo AC) outcskpsidcSAcSJ_2_1111111211211111[color=#40805f,
+                                                       process="out('c',<sk($p.1), sid.1, c_SA.1, c_SJ.1>);"]:
+     [
+     Semistate_11111112112111111( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ),
+     Ack( 'c', <sk($p), sid, c_SA, c_SJ> )
+     ]
+    -->
+     [ State_11111112112111111( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+  */
+
+rule (modulo E) ifpx_1_111111121121111[color=#40805f,
+                                       process="if $p.1=$x.1"]:
+   [
+   State_111111121121111( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 )
+   ]
+  --[ Pred_Not_Eq( $p.1, $x.1 ) ]->
+   [
+   State_1111111211211112( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 )
+   ]
+
+  /*
+  rule (modulo AC) ifpx_1_111111121121111[color=#40805f,
+                                          process="if $p.1=$x.1"]:
+     [ State_111111121121111( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+    --[ Pred_Not_Eq( $p, $x ) ]->
+     [ State_1111111211211112( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+  */
+
+rule (modulo E) ifpy_0_1111111211211112[color=#40805f,
+                                        process="if $p.1=$y.1"]:
+   [
+   State_1111111211211112( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 )
+   ]
+  --[ Pred_Eq( $p.1, $y.1 ) ]->
+   [
+   State_11111112112111121( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1
+   )
+   ]
+
+  /*
+  rule (modulo AC) ifpy_0_1111111211211112[color=#40805f,
+                                           process="if $p.1=$y.1"]:
+     [ State_1111111211211112( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+    --[ Pred_Eq( $p, $y ) ]->
+     [ State_11111112112111121( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+  */
+
+rule (modulo E) outcskpsidcSAcAJ_1_11111112112111121[color=#40805f,
+                                                     process="out('c',<sk($p.1), sid.1, c_SA.1, c_AJ.1>);"]:
+   [
+   State_11111112112111121( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1
+   )
+   ]
+  -->
+   [
+   Message( 'c', <sk($p.1), sid.1, c_SA.1, c_AJ.1> ),
+   Semistate_111111121121111211( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1,
+                                 sid.1
+   )
+   ]
+
+  /*
+  rule (modulo AC) outcskpsidcSAcAJ_1_11111112112111121[color=#40805f,
+                                                        process="out('c',<sk($p.1), sid.1, c_SA.1, c_AJ.1>);"]:
+     [ State_11111112112111121( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+    -->
+     [
+     Message( 'c', <sk($p), sid, c_SA, c_AJ> ),
+     Semistate_111111121121111211( $p, $x, $y, c_AJ, c_SA, c_SJ, sid )
+     ]
+  */
+
+rule (modulo E) outcskpsidcSAcAJ_0_11111112112111121[color=#40805f,
+                                                     process="out('c',<sk($p.1), sid.1, c_SA.1, c_AJ.1>);"]:
+   [
+   State_11111112112111121( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1
+   ),
+   In( 'c' )
+   ]
+  -->
+   [
+   Out( <sk($p.1), sid.1, c_SA.1, c_AJ.1> ),
+   State_111111121121111211( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1
+   )
+   ]
+
+  /*
+  rule (modulo AC) outcskpsidcSAcAJ_0_11111112112111121[color=#40805f,
+                                                        process="out('c',<sk($p.1), sid.1, c_SA.1, c_AJ.1>);"]:
+     [ State_11111112112111121( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ), In( 'c' )
+     ]
+    -->
+     [
+     Out( <sk($p), sid, c_SA, c_AJ> ),
+     State_111111121121111211( $p, $x, $y, c_AJ, c_SA, c_SJ, sid )
+     ]
+  */
+
+rule (modulo E) outcskpsidcSAcAJ_2_11111112112111121[color=#40805f,
+                                                     process="out('c',<sk($p.1), sid.1, c_SA.1, c_AJ.1>);"]:
+   [
+   Semistate_111111121121111211( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1,
+                                 sid.1
+   ),
+   Ack( 'c', <sk($p.1), sid.1, c_SA.1, c_AJ.1> )
+   ]
+  -->
+   [
+   State_111111121121111211( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1
+   )
+   ]
+
+  /*
+  rule (modulo AC) outcskpsidcSAcAJ_2_11111112112111121[color=#40805f,
+                                                        process="out('c',<sk($p.1), sid.1, c_SA.1, c_AJ.1>);"]:
+     [
+     Semistate_111111121121111211( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ),
+     Ack( 'c', <sk($p), sid, c_SA, c_AJ> )
+     ]
+    -->
+     [ State_111111121121111211( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+  */
+
+rule (modulo E) ifpy_1_1111111211211112[color=#40805f,
+                                        process="if $p.1=$y.1"]:
+   [
+   State_1111111211211112( $p.1, $x.1, $y.1, c_AJ.1, c_SA.1, c_SJ.1, sid.1 )
+   ]
+  --[ Pred_Not_Eq( $p.1, $y.1 ) ]->
+   [ ]
+
+  /*
+  rule (modulo AC) ifpy_1_1111111211211112[color=#40805f,
+                                           process="if $p.1=$y.1"]:
+     [ State_1111111211211112( $p, $x, $y, c_AJ, c_SA, c_SJ, sid ) ]
+    --[ Pred_Not_Eq( $p, $y ) ]->
+     [ ]
+  */
+
+restriction predicate_eq:
+  "∀ #i a b. (Pred_Eq( a, b ) @ #i) ⇒ (a = b)"
+  // safety formula
+
+restriction predicate_not_eq:
+  "∀ #i a b. (Pred_Not_Eq( a, b ) @ #i) ⇒ (¬(a = b))"
+  // safety formula
+
+restriction single_session:
+  "∀ #i #j. ((Init( ) @ #i) ∧ (Init( ) @ #j)) ⇒ (#i = #j)"
+  // safety formula
+
+lemma acc_blamed_suff:
+  exists-trace
+  "∃ x sid #i.
+    ((Blame( sid, x ) @ #i) ∧
+     (∀ x.1 sid.1 #i.1. (Blame( sid.1, x.1 ) @ #i.1) ⇒ (x.1 = x))) ∧
+    (∀ a #i.1. (Corrupted( a ) @ #i.1) ⇒ (a = x))"
+/*
+guarded formula characterizing all satisfying traces:
+"∃ x sid #i.
+  (Blame( sid, x ) @ #i)
+ ∧
+  (∀ x.1 sid.1 #i.1. (Blame( sid.1, x.1 ) @ #i.1) ⇒ x.1 = x) ∧
+  (∀ a #i.1. (Corrupted( a ) @ #i.1) ⇒ a = x)"
+*/
+simplify
+solve( State_11111112111211111121( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a,
+                                   sig1_s, sig2_s, sig_a, v_a, v_s, sid_s
+       ) ▶₀ #i )
+  case eventUnequalsid_0_1111111211121111112_case_01
+  solve( State_11111112111211111121( $x, $y.1, c_AJ, c_SA.1, c_SJ.1, ~n.3,
+                                     sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.13 )
+      case incSAsidsvsigs_2_11111112111121
+      solve( !KU( ~n.1 ) @ #vk )
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.11 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.16 )
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            solve( !KU( ~n.3 ) @ #vk.18 )
+              case outcSAsidvsigsidvskx_0_111111121111111_case_1
+              SOLVED // trace found
+            qed
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma acc_verif_empty:
+  all-traces
+  "(¬(∃ x sid #i. Blame( sid, x ) @ #i)) ⇒
+   (¬(∃ sid #i. Unequal( sid ) @ #i))"
+/*
+guarded formula characterizing all counter-examples:
+"(∀ x sid #i. (Blame( sid, x ) @ #i) ⇒ ⊥) ∧
+ (∃ sid #i. (Unequal( sid ) @ #i))"
+*/
+simplify
+by contradiction /* from formulas */
+
+lemma acc_blamed_verif_nonempty:
+  all-traces
+  "∀ x sid #i.
+    (Blame( sid, x ) @ #i) ⇒ (¬(¬(∃ sid.1 #i.1. Unequal( sid.1 ) @ #i.1)))"
+/*
+guarded formula characterizing all counter-examples:
+"∃ x sid #i.
+  (Blame( sid, x ) @ #i) ∧ ∀ sid.1 #i.1. (Unequal( sid.1 ) @ #i.1) ⇒ ⊥"
+*/
+simplify
+solve( State_11111112111211111121( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a,
+                                   sig1_s, sig2_s, sig_a, v_a, v_s, sid_s
+       ) ▶₀ #i )
+  case eventUnequalsid_0_1111111211121111112_case_01
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_02
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_03
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_04
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_05
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_06
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_07
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_08
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_09
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_10
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_11
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_12
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_13
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_14
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_15
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_16
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_17
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_18
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_19
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_20
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_21
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_22
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_23
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_24
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_25
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_26
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_27
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_28
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_29
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_30
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_31
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_32
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_33
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_34
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_35
+  by contradiction /* from formulas */
+next
+  case eventUnequalsid_0_1111111211121111112_case_36
+  by contradiction /* from formulas */
+qed
+
+lemma acc_blamed_min:
+  all-traces
+  "∀ x sid #i.
+    (Blame( sid, x ) @ #i) ⇒
+    (¬(∃ x.1 sid.1 #i.1.
+        (Blame( sid.1, x.1 ) @ #i.1) ∧ ((x.1 = x) ∧ (¬(x = x.1)))))"
+/*
+guarded formula characterizing all counter-examples:
+"∃ x sid #i.
+  (Blame( sid, x ) @ #i)
+ ∧
+  ∃ x.1 sid.1 #i.1. (Blame( sid.1, x.1 ) @ #i.1) ∧ (x.1 = x) ∧ ¬(x = x.1)"
+*/
+simplify
+by contradiction /* from formulas */
+
+lemma acc_blamed_uniq:
+  all-traces
+  "∀ x sid #i. (Blame( sid, x ) @ #i) ⇒ (∃ #i.1. Corrupted( x ) @ #i.1)"
+/*
+guarded formula characterizing all counter-examples:
+"∃ x sid #i.
+  (Blame( sid, x ) @ #i) ∧ ∀ #i.1. (Corrupted( x ) @ #i.1) ⇒ ⊥"
+*/
+simplify
+solve( State_11111112111211111121( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a,
+                                   sig1_s, sig2_s, sig_a, v_a, v_s, sid_s
+       ) ▶₀ #i )
+  case eventUnequalsid_0_1111111211121111112_case_01
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.13 )
+      case incSAsidsvsigs_2_11111112111121
+      solve( !KU( ~n.1 ) @ #vk )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.25, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.25, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_1
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.28 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_2
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.11 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.16 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_3
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.28 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_4
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.11 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.16 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_02
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.13 )
+      case incSAsidsvsigs_0_11111112111121
+      by contradiction /* from formulas */
+    next
+      case incSAsidsvsigs_2_11111112111121
+      by solve( Ack( ~n.1, <<~n.3, v_s>, sig(<~n.3, v_s>, sk($x))>
+                ) ▶₁ #vr.15 )
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_03
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.13 )
+      case incSAsidsvsigs_2_11111112111121
+      solve( !KU( ~n.1 ) @ #vk )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.25, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.25, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_1
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.28 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_2
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.11 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.16 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_3
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.28 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_4
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.11 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.16 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_04
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.13 )
+      case incSAsidsvsigs_0_11111112111121
+      by contradiction /* from formulas */
+    next
+      case incSAsidsvsigs_2_11111112111121
+      by solve( Ack( ~n.1, <<~n.3, v_s>, sig(<~n.3, v_s>, sk($x))>
+                ) ▶₁ #vr.15 )
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_05
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.2
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                $x, $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.12 )
+      case incSAsidsvsigs_0_11111112111121
+      solve( !KU( ~n.2 ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    next
+      case incSAsidsvsigs_2_11111112111121
+      solve( !KU( ~n.2 ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_06
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.2
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                $x, $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.12 )
+      case incSAsidsvsigs_0_11111112111121
+      solve( !KU( ~n.2 ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    next
+      case incSAsidsvsigs_2_11111112111121
+      solve( !KU( ~n.2 ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_07
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.13 )
+      case incSAsidsvsigs_2_11111112111121
+      solve( !KU( ~n.1 ) @ #vk )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.25, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.25, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_1
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.28 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_2
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.11 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.16 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_3
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.28 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_4
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.11 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.16 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_08
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.13 )
+      case incSAsidsvsigs_0_11111112111121
+      by contradiction /* from formulas */
+    next
+      case incSAsidsvsigs_2_11111112111121
+      by solve( Ack( ~n.1, <<~n.3, v_s>, sig(<~n.3, v_s>, sk($x))>
+                ) ▶₁ #vr.15 )
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_09
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.13 )
+      case incSAsidsvsigs_2_11111112111121
+      solve( !KU( ~n.1 ) @ #vk )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.25, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.25, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_1
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.28 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_2
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.11 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.16 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_3
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.28 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_4
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.11 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.16 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_10
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.13 )
+      case incSAsidsvsigs_0_11111112111121
+      by contradiction /* from formulas */
+    next
+      case incSAsidsvsigs_2_11111112111121
+      by solve( Ack( ~n.1, <<~n.3, v_s>, sig(<~n.3, v_s>, sk($x))>
+                ) ▶₁ #vr.15 )
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_11
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.2
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                $x, $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.12 )
+      case incSAsidsvsigs_0_11111112111121
+      solve( !KU( ~n.2 ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    next
+      case incSAsidsvsigs_2_11111112111121
+      solve( !KU( ~n.2 ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_12
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.2
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                $x, $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.12 )
+      case incSAsidsvsigs_0_11111112111121
+      solve( !KU( ~n.2 ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    next
+      case incSAsidsvsigs_2_11111112111121
+      solve( !KU( ~n.2 ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_13
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA, c_SJ, ~n.3,
+                                     sid_a.1, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( !KU( ~n ) @ #vk.1 )
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.20 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.20 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.20 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.20 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.21, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.21, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.20, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.20, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.20, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.20, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_1
+      by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.24 )
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_2
+      solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+        case c_sig
+        solve( !KU( sk($x) ) @ #vk.19 )
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_4
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_4
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                    $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                    $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcSAsidvsigsidvskx_0_111111121111111
+        by contradiction /* from formulas */
+      qed
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_3
+      by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.24 )
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_4
+      solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+        case c_sig
+        solve( !KU( sk($x) ) @ #vk.19 )
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_4
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_4
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                    $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                    $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcSAsidvsigsidvskx_0_111111121111111
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_14
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA, c_SJ, ~n.3,
+                                     sid_a.1, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Ack( ~n.1, <<~n.3, v_s>, sig(<~n.3, v_s>, sk($x))> ) ▶₁ #vr.12 )
+      case incSAsidsvsigs_0_11111112111121
+      solve( !KU( ~n ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.22 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.20, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.20, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.22 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.20, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.20, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.22 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.22 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_1
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.26 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_2
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.18 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                      $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                      $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_3
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.26 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_4
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.18 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                      $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                      $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        qed
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_15
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA, c_SJ, ~n.3,
+                                     sid_a.1, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( !KU( ~n ) @ #vk.1 )
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.17 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.15, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.15, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.17 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.15, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.15, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.17 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.17 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.17, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.17, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.17, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.17, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_1
+      by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.21 )
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_2
+      solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+        case c_sig
+        solve( !KU( sk($x) ) @ #vk.24 )
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_4
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_4
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                    $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( ~n.2 ) @ #vk.10 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                    $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( ~n.2 ) @ #vk.10 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* from formulas */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* from formulas */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcSAsidvsigsidvskx_0_111111121111111
+        solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+          case c_sig
+          solve( !KU( ~n.2 ) @ #vk.11 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.30 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.30 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcSJsidvsigsidvskx_0_1111111211111111_case_1
+        solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+          case c_sig
+          solve( !KU( ~n.2 ) @ #vk.11 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.32, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.32, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.31 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.31 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSJsidvsigsidvskx_0_1111111211111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcSJsidvsigsidvskx_0_1111111211111111_case_2
+        solve( Ack( ~n.1, <<~n.3, v_a>, sig(<~n.3, v_a>, sk($x))> ) ▶₁ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+            case c_sig
+            solve( !KU( ~n.2 ) @ #vk.11 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                           >,
+                                           $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                      ) ▶₀ #vr.33 )
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                           >,
+                                           $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                      ) ▶₀ #vr.33 )
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                        $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              solve( !KU( ~n.2 ) @ #vk.10 )
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_1
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_2
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_3
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_4
+                by contradiction /* from formulas */
+              qed
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                        $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              solve( !KU( ~n.2 ) @ #vk.10 )
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_1
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_2
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_3
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_4
+                by contradiction /* from formulas */
+              qed
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcSJsidvsigsidvskx_0_1111111211111111
+            by contradiction /* from formulas */
+          qed
+        qed
+      qed
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_3
+      by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.21 )
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_4
+      solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+        case c_sig
+        solve( !KU( sk($x) ) @ #vk.24 )
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_4
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_4
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                    $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( ~n.2 ) @ #vk.10 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                    $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( ~n.2 ) @ #vk.10 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* from formulas */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* from formulas */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcSAsidvsigsidvskx_0_111111121111111
+        solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+          case c_sig
+          solve( !KU( ~n.2 ) @ #vk.11 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.30 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.30 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcSJsidvsigsidvskx_0_1111111211111111_case_1
+        solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+          case c_sig
+          solve( !KU( ~n.2 ) @ #vk.11 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.32, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.32, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.31 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.31 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSJsidvsigsidvskx_0_1111111211111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcSJsidvsigsidvskx_0_1111111211111111_case_2
+        solve( Ack( ~n.1, <<~n.3, v_a>, sig(<~n.3, v_a>, sk($x))> ) ▶₁ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+            case c_sig
+            solve( !KU( ~n.2 ) @ #vk.11 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                           >,
+                                           $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                      ) ▶₀ #vr.33 )
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                           >,
+                                           $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                      ) ▶₀ #vr.33 )
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                        $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              solve( !KU( ~n.2 ) @ #vk.10 )
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_1
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_2
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_3
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_4
+                by contradiction /* from formulas */
+              qed
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                        $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              solve( !KU( ~n.2 ) @ #vk.10 )
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_1
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_2
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_3
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_4
+                by contradiction /* from formulas */
+              qed
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcSJsidvsigsidvskx_0_1111111211111111
+            by contradiction /* from formulas */
+          qed
+        qed
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_16
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA, c_SJ, ~n.3,
+                                     sid_a.1, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( !KU( ~n ) @ #vk.1 )
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.20 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.20 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.20 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.20 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.21, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.21, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.20, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.20, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.20, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.20, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_1
+      by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.24 )
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_2
+      solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+        case c_sig
+        solve( !KU( sk($x) ) @ #vk.19 )
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_4
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_4
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                    $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                    $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcSAsidvsigsidvskx_0_111111121111111
+        by contradiction /* from formulas */
+      qed
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_3
+      by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.24 )
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_4
+      solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+        case c_sig
+        solve( !KU( sk($x) ) @ #vk.19 )
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_4
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_4
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                    $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                    $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcSAsidvsigsidvskx_0_111111121111111
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_17
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA, c_SJ, ~n.3,
+                                     sid_a.1, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Ack( ~n.1, <<~n.3, v_s>, sig(<~n.3, v_s>, sk($x))> ) ▶₁ #vr.12 )
+      case incSAsidsvsigs_0_11111112111121
+      solve( !KU( ~n ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.22 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.20, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.20, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.22 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.20, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.20, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.22 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.22 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_1
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.26 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_2
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.18 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                      $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                      $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_3
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.26 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_4
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.18 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                      $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                      $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        qed
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_18
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA, c_SJ, ~n.3,
+                                     sid_a.1, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( !KU( ~n ) @ #vk.1 )
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.17 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.15, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.15, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.17 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.15, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.15, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.17 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.17 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.17, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.17, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.17, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.17, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_1
+      by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.21 )
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_2
+      solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+        case c_sig
+        solve( !KU( sk($x) ) @ #vk.24 )
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_4
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_4
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                    $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( ~n.2 ) @ #vk.10 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                    $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( ~n.2 ) @ #vk.10 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* from formulas */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* from formulas */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcSAsidvsigsidvskx_0_111111121111111
+        solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+          case c_sig
+          solve( !KU( ~n.2 ) @ #vk.11 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.30 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.30 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcSJsidvsigsidvskx_0_1111111211111111_case_1
+        solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+          case c_sig
+          solve( !KU( ~n.2 ) @ #vk.11 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.32, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.32, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.31 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.31 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSJsidvsigsidvskx_0_1111111211111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcSJsidvsigsidvskx_0_1111111211111111_case_2
+        solve( Ack( ~n.1, <<~n.3, v_a>, sig(<~n.3, v_a>, sk($x))> ) ▶₁ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+            case c_sig
+            solve( !KU( ~n.2 ) @ #vk.11 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                           >,
+                                           $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                      ) ▶₀ #vr.33 )
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                           >,
+                                           $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                      ) ▶₀ #vr.33 )
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                        $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              solve( !KU( ~n.2 ) @ #vk.10 )
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_1
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_2
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_3
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_4
+                by contradiction /* from formulas */
+              qed
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                        $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              solve( !KU( ~n.2 ) @ #vk.10 )
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_1
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_2
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_3
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_4
+                by contradiction /* from formulas */
+              qed
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcSJsidvsigsidvskx_0_1111111211111111
+            by contradiction /* from formulas */
+          qed
+        qed
+      qed
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_3
+      by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.21 )
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_4
+      solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+        case c_sig
+        solve( !KU( sk($x) ) @ #vk.24 )
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_4
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_4
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                    $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( ~n.2 ) @ #vk.10 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                    $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( ~n.2 ) @ #vk.10 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* from formulas */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* from formulas */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcSAsidvsigsidvskx_0_111111121111111
+        solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+          case c_sig
+          solve( !KU( ~n.2 ) @ #vk.11 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.30 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.30 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcSJsidvsigsidvskx_0_1111111211111111_case_1
+        solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+          case c_sig
+          solve( !KU( ~n.2 ) @ #vk.11 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.32, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.32, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.31 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.31 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSJsidvsigsidvskx_0_1111111211111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcSJsidvsigsidvskx_0_1111111211111111_case_2
+        solve( Ack( ~n.1, <<~n.3, v_a>, sig(<~n.3, v_a>, sk($x))> ) ▶₁ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+            case c_sig
+            solve( !KU( ~n.2 ) @ #vk.11 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                           >,
+                                           $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                      ) ▶₀ #vr.33 )
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                           >,
+                                           $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                      ) ▶₀ #vr.33 )
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                        $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              solve( !KU( ~n.2 ) @ #vk.10 )
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_1
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_2
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_3
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_4
+                by contradiction /* from formulas */
+              qed
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                        $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              solve( !KU( ~n.2 ) @ #vk.10 )
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_1
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_2
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_3
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_4
+                by contradiction /* from formulas */
+              qed
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcSJsidvsigsidvskx_0_1111111211111111
+            by contradiction /* from formulas */
+          qed
+        qed
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_19
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.13 )
+      case incSAsidsvsigs_2_11111112111121
+      solve( !KU( ~n.1 ) @ #vk )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.25, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.25, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_1
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.28 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_2
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.11 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.16 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_3
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.28 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_4
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.11 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.16 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_20
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.13 )
+      case incSAsidsvsigs_0_11111112111121
+      by contradiction /* from formulas */
+    next
+      case incSAsidsvsigs_2_11111112111121
+      by solve( Ack( ~n.1, <<~n.3, v_s>, sig(<~n.3, v_s>, sk($x))>
+                ) ▶₁ #vr.15 )
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_21
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.13 )
+      case incSAsidsvsigs_2_11111112111121
+      solve( !KU( ~n.1 ) @ #vk )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.25, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.25, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_1
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.28 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_2
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.11 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.16 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_3
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.28 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_4
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.11 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.16 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_22
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.13 )
+      case incSAsidsvsigs_0_11111112111121
+      by contradiction /* from formulas */
+    next
+      case incSAsidsvsigs_2_11111112111121
+      by solve( Ack( ~n.1, <<~n.3, v_s>, sig(<~n.3, v_s>, sk($x))>
+                ) ▶₁ #vr.15 )
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_23
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.2
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                $x, $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.12 )
+      case incSAsidsvsigs_0_11111112111121
+      solve( !KU( ~n.2 ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    next
+      case incSAsidsvsigs_2_11111112111121
+      solve( !KU( ~n.2 ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_24
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.2
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                $x, $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.12 )
+      case incSAsidsvsigs_0_11111112111121
+      solve( !KU( ~n.2 ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    next
+      case incSAsidsvsigs_2_11111112111121
+      solve( !KU( ~n.2 ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_25
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.13 )
+      case incSAsidsvsigs_2_11111112111121
+      solve( !KU( ~n.1 ) @ #vk )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.25, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.25, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_1
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.28 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_2
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.11 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.16 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_3
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.28 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_4
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.11 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.16 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_26
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.13 )
+      case incSAsidsvsigs_0_11111112111121
+      by contradiction /* from formulas */
+    next
+      case incSAsidsvsigs_2_11111112111121
+      by solve( Ack( ~n.1, <<~n.3, v_s>, sig(<~n.3, v_s>, sk($x))>
+                ) ▶₁ #vr.15 )
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_27
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.13 )
+      case incSAsidsvsigs_2_11111112111121
+      solve( !KU( ~n.1 ) @ #vk )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.25, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.25, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.26 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_1
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.28 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_2
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.11 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.16 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_3
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.28 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_4
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.11 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.16 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.36 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))
+                                         >,
+                                         $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, 
+                                          sig(<~n.3, v_a>, sk($x.1))>,
+                                         $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.34 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.36 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_28
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.13 )
+      case incSAsidsvsigs_0_11111112111121
+      by contradiction /* from formulas */
+    next
+      case incSAsidsvsigs_2_11111112111121
+      by solve( Ack( ~n.1, <<~n.3, v_s>, sig(<~n.3, v_s>, sk($x))>
+                ) ▶₁ #vr.15 )
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_29
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.2
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                $x, $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.12 )
+      case incSAsidsvsigs_0_11111112111121
+      solve( !KU( ~n.2 ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    next
+      case incSAsidsvsigs_2_11111112111121
+      solve( !KU( ~n.2 ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_30
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA.1, c_SJ.1,
+                                     ~n.3, sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.2
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                $x, $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.12 )
+      case incSAsidsvsigs_0_11111112111121
+      solve( !KU( ~n.2 ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.24, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    next
+      case incSAsidsvsigs_2_11111112111121
+      solve( !KU( ~n.2 ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.19, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.21 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.21, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.23 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_1
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_2
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_3
+        by contradiction /* from formulas */
+      next
+        case outcskpsidcSAcSJ_0_1111111211211111_case_4
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_31
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA, c_SJ, ~n.3,
+                                     sid_a.1, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( !KU( ~n ) @ #vk.1 )
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.20 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.20 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.20 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.20 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.21, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.21, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.20, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.20, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.20, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.20, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_1
+      by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.24 )
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_2
+      solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+        case c_sig
+        solve( !KU( sk($x) ) @ #vk.19 )
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_4
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_4
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                    $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                    $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcSAsidvsigsidvskx_0_111111121111111
+        by contradiction /* from formulas */
+      qed
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_3
+      by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.24 )
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_4
+      solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+        case c_sig
+        solve( !KU( sk($x) ) @ #vk.19 )
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_4
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_4
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                    $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                    $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcSAsidvsigsidvskx_0_111111121111111
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_32
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA, c_SJ, ~n.3,
+                                     sid_a.1, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Ack( ~n.1, <<~n.3, v_s>, sig(<~n.3, v_s>, sk($x))> ) ▶₁ #vr.12 )
+      case incSAsidsvsigs_0_11111112111121
+      solve( !KU( ~n ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.22 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.20, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.20, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.22 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.20, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.20, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.22 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.22 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_1
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.26 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_2
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.18 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                      $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                      $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_3
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.26 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_4
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.18 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                      $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                      $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        qed
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_33
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA, c_SJ, ~n.3,
+                                     sid_a.1, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( !KU( ~n ) @ #vk.1 )
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.17 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.15, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.15, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.17 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.15, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.15, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.17 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.17 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.17, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.17, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.17, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.17, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_1
+      by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.21 )
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_2
+      solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+        case c_sig
+        solve( !KU( sk($x) ) @ #vk.24 )
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_4
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_4
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                    $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( ~n.2 ) @ #vk.10 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                    $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( ~n.2 ) @ #vk.10 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* from formulas */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* from formulas */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcSAsidvsigsidvskx_0_111111121111111
+        solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+          case c_sig
+          solve( !KU( ~n.2 ) @ #vk.11 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.30 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.30 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcSJsidvsigsidvskx_0_1111111211111111_case_1
+        solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+          case c_sig
+          solve( !KU( ~n.2 ) @ #vk.11 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.32, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.32, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.31 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.31 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSJsidvsigsidvskx_0_1111111211111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcSJsidvsigsidvskx_0_1111111211111111_case_2
+        solve( Ack( ~n.1, <<~n.3, v_a>, sig(<~n.3, v_a>, sk($x))> ) ▶₁ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+            case c_sig
+            solve( !KU( ~n.2 ) @ #vk.11 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                           >,
+                                           $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                      ) ▶₀ #vr.33 )
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                           >,
+                                           $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                      ) ▶₀ #vr.33 )
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                        $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              solve( !KU( ~n.2 ) @ #vk.10 )
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_1
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_2
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_3
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_4
+                by contradiction /* from formulas */
+              qed
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                        $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              solve( !KU( ~n.2 ) @ #vk.10 )
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_1
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_2
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_3
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_4
+                by contradiction /* from formulas */
+              qed
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcSJsidvsigsidvskx_0_1111111211111111
+            by contradiction /* from formulas */
+          qed
+        qed
+      qed
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_3
+      by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.21 )
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_4
+      solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+        case c_sig
+        solve( !KU( sk($x) ) @ #vk.24 )
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_4
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_4
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                    $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( ~n.2 ) @ #vk.10 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                    $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( ~n.2 ) @ #vk.10 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* from formulas */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* from formulas */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcSAsidvsigsidvskx_0_111111121111111
+        solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+          case c_sig
+          solve( !KU( ~n.2 ) @ #vk.11 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.30 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.30 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcSJsidvsigsidvskx_0_1111111211111111_case_1
+        solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+          case c_sig
+          solve( !KU( ~n.2 ) @ #vk.11 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.32, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.32, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.31 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.31 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSJsidvsigsidvskx_0_1111111211111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcSJsidvsigsidvskx_0_1111111211111111_case_2
+        solve( Ack( ~n.1, <<~n.3, v_a>, sig(<~n.3, v_a>, sk($x))> ) ▶₁ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+            case c_sig
+            solve( !KU( ~n.2 ) @ #vk.11 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                           >,
+                                           $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                      ) ▶₀ #vr.33 )
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                           >,
+                                           $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                      ) ▶₀ #vr.33 )
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                        $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              solve( !KU( ~n.2 ) @ #vk.10 )
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_1
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_2
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_3
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_4
+                by contradiction /* from formulas */
+              qed
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                        $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              solve( !KU( ~n.2 ) @ #vk.10 )
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_1
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_2
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_3
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_4
+                by contradiction /* from formulas */
+              qed
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcSJsidvsigsidvskx_0_1111111211111111
+            by contradiction /* from formulas */
+          qed
+        qed
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_34
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA, c_SJ, ~n.3,
+                                     sid_a.1, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( !KU( ~n ) @ #vk.1 )
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.20 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.20 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.20 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.20 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.21, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.21, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.20, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.20, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.20, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.20, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+      solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                  $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.22 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_1
+      by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.24 )
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_2
+      solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+        case c_sig
+        solve( !KU( sk($x) ) @ #vk.19 )
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_4
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_4
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                    $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                    $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcSAsidvsigsidvskx_0_111111121111111
+        by contradiction /* from formulas */
+      qed
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_3
+      by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.24 )
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_4
+      solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+        case c_sig
+        solve( !KU( sk($x) ) @ #vk.19 )
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_4
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_4
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                    $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                    $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.30 )
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.32 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcSAsidvsigsidvskx_0_111111121111111
+        by contradiction /* from formulas */
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_35
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA, c_SJ, ~n.3,
+                                     sid_a.1, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Ack( ~n.1, <<~n.3, v_s>, sig(<~n.3, v_s>, sk($x))> ) ▶₁ #vr.12 )
+      case incSAsidsvsigs_0_11111112111121
+      solve( !KU( ~n ) @ #vk.1 )
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.22 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.20, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.20, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.22 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.20, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.20, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.22 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.22 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.23, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by solve( (#vr.22, 0) ~~> (#vk, 0) )
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                    $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.24 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_1
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.26 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_2
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.18 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                      $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                      $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        qed
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_3
+        by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.26 )
+      next
+        case outcskpsidcSAcAJ_0_11111112112111121_case_4
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.18 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                        $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.34 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcAJ_0_11111112112111121_case_4
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                      $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                      $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s, v>, sig(<sid, v>, sk($x.1))>, $x.1,
+                                      $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.34 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        qed
+      qed
+    qed
+  qed
+next
+  case eventUnequalsid_0_1111111211121111112_case_36
+  solve( State_11111112111211111121( $x.1, $y.1, c_AJ, c_SA, c_SJ, ~n.3,
+                                     sid_a.1, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( !KU( ~n ) @ #vk.1 )
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.17 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.15, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.15, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.17 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.15, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.15, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.17 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.17 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.18, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.17, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.17, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by solve( (#vr.17, 0) ~~> (#vk, 0) )
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by solve( (#vr.17, 0) ~~> (#vk, 0) )
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+      solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                  $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+             ) ▶₀ #vr.19 )
+        case incSAsidsvsigs_0_11111112111121
+        by contradiction /* cyclic */
+      next
+        case incSAsidsvsigs_2_11111112111121
+        by contradiction /* cyclic */
+      qed
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_1
+      by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.21 )
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_2
+      solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+        case c_sig
+        solve( !KU( sk($x) ) @ #vk.24 )
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_4
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_4
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                    $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( ~n.2 ) @ #vk.10 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                    $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( ~n.2 ) @ #vk.10 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* from formulas */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* from formulas */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcSAsidvsigsidvskx_0_111111121111111
+        solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+          case c_sig
+          solve( !KU( ~n.2 ) @ #vk.11 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.30 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.30 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcSJsidvsigsidvskx_0_1111111211111111_case_1
+        solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+          case c_sig
+          solve( !KU( ~n.2 ) @ #vk.11 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.32, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.32, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.31 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.31 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSJsidvsigsidvskx_0_1111111211111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcSJsidvsigsidvskx_0_1111111211111111_case_2
+        solve( Ack( ~n.1, <<~n.3, v_a>, sig(<~n.3, v_a>, sk($x))> ) ▶₁ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+            case c_sig
+            solve( !KU( ~n.2 ) @ #vk.11 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                           >,
+                                           $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                      ) ▶₀ #vr.33 )
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                           >,
+                                           $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                      ) ▶₀ #vr.33 )
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                        $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              solve( !KU( ~n.2 ) @ #vk.10 )
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_1
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_2
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_3
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_4
+                by contradiction /* from formulas */
+              qed
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                        $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              solve( !KU( ~n.2 ) @ #vk.10 )
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_1
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_2
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_3
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_4
+                by contradiction /* from formulas */
+              qed
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcSJsidvsigsidvskx_0_1111111211111111
+            by contradiction /* from formulas */
+          qed
+        qed
+      qed
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_3
+      by solve( Message( 'c', <'corrupt', $y> ) ▶₁ #vr.21 )
+    next
+      case outcskpsidcSAcAJ_0_11111112112111121_case_4
+      solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.7 )
+        case c_sig
+        solve( !KU( sk($x) ) @ #vk.24 )
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.27 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.29 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcAJ_0_11111112112111121_case_4
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_1
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_2
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_3
+          by contradiction /* from formulas */
+        next
+          case outcskpsidcSAcSJ_0_1111111211211111_case_4
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                    $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( ~n.2 ) @ #vk.10 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x))>,
+                                    $x, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( ~n.2 ) @ #vk.10 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.33, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.36, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.35, 0) ~~> (#vk.2, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.37 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* from formulas */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+        solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                    $x.1, $x, c_AJ, c_SA, c_SJ, ~n.3
+               ) ▶₀ #vr.27 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* from formulas */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* impossible chain */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* impossible chain */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+        solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                    $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+               ) ▶₀ #vr.29 )
+          case incSAsidsvsigs_0_11111112111121
+          by contradiction /* cyclic */
+        next
+          case incSAsidsvsigs_2_11111112111121
+          by contradiction /* cyclic */
+        qed
+      next
+        case outcSAsidvsigsidvskx_0_111111121111111
+        solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+          case c_sig
+          solve( !KU( ~n.2 ) @ #vk.11 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.28, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.30 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.30, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.32 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.30 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.30 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.30 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.36 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.38 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.32 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSAsidvsigsidvskx_0_111111121111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcSJsidvsigsidvskx_0_1111111211111111_case_1
+        solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+          case c_sig
+          solve( !KU( ~n.2 ) @ #vk.11 )
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.29, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.31 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.32, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.32, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_1
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_2
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_3
+            by contradiction /* from formulas */
+          next
+            case outcskpsidcSAcSJ_0_1111111211211111_case_4
+            by contradiction /* from formulas */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.31 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+          by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                         >,
+                                         $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                    ) ▶₀ #vr.31 )
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+          solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                      $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                 ) ▶₀ #vr.31 )
+            case incSAsidsvsigs_2_11111112111121
+            solve( !KU( ~n.2 ) @ #vk.12 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.35, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.37 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.37, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.2, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.39 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* impossible chain */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* impossible chain */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+          solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                      $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                 ) ▶₀ #vr.33 )
+            case incSAsidsvsigs_0_11111112111121
+            by contradiction /* cyclic */
+          next
+            case incSAsidsvsigs_2_11111112111121
+            by contradiction /* cyclic */
+          qed
+        next
+          case outcSJsidvsigsidvskx_0_1111111211111111
+          by contradiction /* from formulas */
+        qed
+      next
+        case outcSJsidvsigsidvskx_0_1111111211111111_case_2
+        solve( Ack( ~n.1, <<~n.3, v_a>, sig(<~n.3, v_a>, sk($x))> ) ▶₁ #vr.25 )
+          case incSAsidsvsigs_0_11111112111121
+          solve( !KU( sig(<~n.3, v_a>, sk($y)) ) @ #vk.8 )
+            case c_sig
+            solve( !KU( ~n.2 ) @ #vk.11 )
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.31, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.33 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.34, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by solve( (#vr.33, 0) ~~> (#vk.3, 0) )
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+              solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                          $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                     ) ▶₀ #vr.35 )
+                case incSAsidsvsigs_0_11111112111121
+                by contradiction /* cyclic */
+              next
+                case incSAsidsvsigs_2_11111112111121
+                by contradiction /* cyclic */
+              qed
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_1
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_2
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_3
+              by contradiction /* from formulas */
+            next
+              case outcskpsidcSAcSJ_0_1111111211211111_case_4
+              by contradiction /* from formulas */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+            by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                           >,
+                                           $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                      ) ▶₀ #vr.33 )
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+            by solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($y))
+                                           >,
+                                           $y, $y.1, c_AJ, c_SA, c_SJ, ~n.3
+                      ) ▶₀ #vr.33 )
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+            solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                        $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              solve( !KU( ~n.2 ) @ #vk.10 )
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_1
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_2
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_3
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_4
+                by contradiction /* from formulas */
+              qed
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+            solve( Let_111111121111211( <<sid_s.1, v_a>, sig(<~n.3, v_a>, sk($x.1))>,
+                                        $x.1, $y, c_AJ, c_SA, c_SJ, ~n.3
+                   ) ▶₀ #vr.33 )
+              case incSAsidsvsigs_0_11111112111121
+              solve( !KU( ~n.2 ) @ #vk.10 )
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_01
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_02
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.36, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_03
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_04
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.38 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_05
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_06
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.39, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_07
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_08
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_09
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_10
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by solve( (#vr.38, 0) ~~> (#vk.3, 0) )
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_11
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcAJsidvsigssigsidvsky_0_1111111211112111_case_12
+                solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                            $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                       ) ▶₀ #vr.40 )
+                  case incSAsidsvsigs_0_11111112111121
+                  by contradiction /* cyclic */
+                next
+                  case incSAsidsvsigs_2_11111112111121
+                  by contradiction /* cyclic */
+                qed
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_1
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_2
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_3
+                by contradiction /* from formulas */
+              next
+                case outcskpsidcSAcSJ_0_1111111211211111_case_4
+                by contradiction /* from formulas */
+              qed
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_13
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_14
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* impossible chain */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* impossible chain */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_15
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcAJsidvsigssigsidvsky_0_1111111211112111_case_16
+            solve( Let_111111121111211( <<sid_s.1, v>, sig(<sid, v>, sk($x.1))>,
+                                        $x.1, $y.1, c_AJ, c_SA, c_SJ, sid
+                   ) ▶₀ #vr.35 )
+              case incSAsidsvsigs_0_11111112111121
+              by contradiction /* cyclic */
+            next
+              case incSAsidsvsigs_2_11111112111121
+              by contradiction /* cyclic */
+            qed
+          next
+            case outcSJsidvsigsidvskx_0_1111111211111111
+            by contradiction /* from formulas */
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+lemma acc_blamed_inj:
+  all-traces "⊤"
+/*
+guarded formula characterizing all counter-examples:
+"⊥"
+*/
+by contradiction /* from formulas */
+
+lemma acc_blamed_single:
+  exists-trace
+  "∃ x sid #i.
+    (Blame( sid, x ) @ #i) ∧
+    (∀ x.1 sid.1 #i.1. (Blame( sid.1, x.1 ) @ #i.1) ⇒ (x.1 = x))"
+/*
+guarded formula characterizing all satisfying traces:
+"∃ x sid #i.
+  (Blame( sid, x ) @ #i)
+ ∧
+  ∀ x.1 sid.1 #i.1. (Blame( sid.1, x.1 ) @ #i.1) ⇒ x.1 = x"
+*/
+simplify
+solve( State_11111112111211111121( $x, $y, c_AJ, c_SA, c_SJ, sid, sid_a,
+                                   sig1_s, sig2_s, sig_a, v_a, v_s, sid_s
+       ) ▶₀ #i )
+  case eventUnequalsid_0_1111111211121111112_case_01
+  solve( State_11111112111211111121( $x, $y.1, c_AJ, c_SA.1, c_SJ.1, ~n.3,
+                                     sid_a, sig1_s, sig2_s, sig_a, v_a.1, v_s.1, sid_s.1
+         ) ▶₀ #j )
+    case eventUnequalsid_0_1111111211121111112
+    solve( Let_111111121111211( <<sid_s, v_a>, sig(<~n.3, v_a>, sk($x))>, $x,
+                                $y, ~n, c_SA, c_SJ, ~n.3
+           ) ▶₀ #vr.13 )
+      case incSAsidsvsigs_2_11111112111121
+      solve( !KU( ~n.1 ) @ #vk )
+        case outcskpsidcSAcAJ_0_11111112112111121_case_2
+        solve( !KU( sig(<~n.3, v_a>, sk($x)) ) @ #vk.11 )
+          case c_sig
+          solve( !KU( sk($x) ) @ #vk.16 )
+            case outcskpsidcSAcAJ_0_11111112112111121_case_2
+            solve( !KU( ~n.3 ) @ #vk.20 )
+              case outcSAsidvsigsidvskx_0_111111121111111_case_1
+              SOLVED // trace found
+            qed
+          qed
+        qed
+      qed
+    qed
+  qed
+qed
+
+predicate: blamed( x )<=>∃ sid #i. Blame( sid, x ) @ #i
+
+/*
+WARNING: the following wellformedness checks failed!
+
+Accountability (RP check)
+  The specification contains at least one restriction.
+  
+  Please verify manually that your protocol fulfills the following condition:
+  
+  For each case test τ, traces t, t’, and instantiations ρ, ρ’:
+  If τ holds on t with ρ, and τ single-matches with ρ’ on t’, then
+  there exists a trace t’’ such that τ single-matches with ρ on t’’
+  and the parties corrupted in t’’ are the same as the parties
+  corrupted in t’ renamed from rng(ρ’) to rng(ρ).
+
+Derivation Checks
+=================
+
+  Derivation checks timed out.
+  Use --derivcheck-timeout=INT to configure timeout.
+  Set to 0 to deactivate for no timeout.
+*/
+
+/*
+Generated from:
+Tamarin version 1.9.0
+Maude version 3.2.2
+Git revision: c838686f5a3d41b6a355eafd32cc2104ca41809c (with uncommited changes), branch: HEAD
+Compiled at: 2023-10-25 11:27:38.363683988 UTC
+*/
+
+end
+/* Output
+
+==============================================================================
+summary of summaries:
+
+analyzed: examples/accountability/csf21-acc-unbounded/previous/whodunit.spthy
+
+  output:          examples/accountability/csf21-acc-unbounded/previous/whodunit.spthy.tmp
+  processing time: 600.27s
+  
+  WARNING: 2 wellformedness check failed!
+           The analysis results might be wrong!
+  
+  acc_blamed_suff (exists-trace): verified (9 steps)
+  acc_verif_empty (all-traces): verified (2 steps)
+  acc_blamed_verif_nonempty (all-traces): verified (38 steps)
+  acc_blamed_min (all-traces): verified (2 steps)
+  acc_blamed_uniq (all-traces): verified (9750 steps)
+  acc_blamed_inj (all-traces): verified (1 steps)
+  acc_blamed_single (exists-trace): verified (9 steps)
+
+==============================================================================
+*/
diff --git a/examples/accountability/csf21-acc-unbounded/README.md b/examples/accountability/csf21-acc-unbounded/README.md
index 55de25169..e800e50d7 100644
--- a/examples/accountability/csf21-acc-unbounded/README.md
+++ b/examples/accountability/csf21-acc-unbounded/README.md
@@ -1,5 +1,16 @@
-This directory contains the Tamarin models of the following paper:
-[1] "Verifying Accountability for Unbounded Sets of Participants", Kevin Morio, and Robert Künnemann, CSF21.
+# Verifying Accountability for Unbounded Sets of Participants
+
+This is the artifact for the paper *Verifying Accountability for Unbounded Sets of Participants* accepted for *CSF '21*.
+
+## Authors
+
+- Kevin Morio, *CISPA Helmholtz Center for Information Security*
+- Robert Künnemann, *CISPA Helmholtz Center for Information Security*
+
+## Paper
+
+The published version of the paper is available under DOI [10.1109/CSF51468.2021.00032](https://doi.org/10.1109/CSF51468.2021.00032).
+The preprint of the full version of the paper is available on arXiv: [2006.12047](https://arxiv.org/abs/2006.12047).
 
 ## Models
 
@@ -31,15 +42,22 @@ This directory contains the Tamarin models of the following paper:
     └── whodunit.spthy
 ```
 
-The directory [mixnets/basic](./mixnets/basic) contains a case study modeling basic decryption mixnets in the limited case where corrupted senders and mix servers can only repost already posted messages.
+### [`mixnets/basic`](./mixnets/basic)
 
-The directory [mixnets/message-tracing](./mixnets/message-tracing) contains two sets of case studies implementing decryption mixnets with the message tracing technique.
+This directory contains a case study modeling basic decryption mixnets in the limited case where corrupted senders and mix servers can only repost already posted messages.
+
+### [`mixnets/message-tracing`](./mixnets/message-tracing)
+
+This directory contains two sets of case studies implementing decryption mixnets with the message tracing technique.
 In the models with the name `dmn-message-tracing-all-<i>.spthy`, the audit continues after detecting the first unexpected message on the bulletin board.
 In the models with the name `dmn-message-tracing-first-<i>.spthy`, the audit stops after detecting the first unexpected message on the bulletin board.
 The number of mix servers in the model is indicated by `<i>`.
 
-The directory [mixvote](./mixvote) contains a variant of the MixVote protocol extended to unbounded sessions for the indicated number of allowed server identities.
+### [`mixvote`](./mixvote)
+
+This directory contains a variant of the MixVote protocol extended to unbounded sessions for the indicated number of allowed server identities.
 The case study is based on the MixVote model [mixvote_SmHh.spthy](https://github.com/tamarin-prover/tamarin-prover/blob/develop/examples/csf20-disputeResolution/mixvote_SmHh.spthy) by Lara Schmid.
 
-The directory [previous](./previous) contains the case studies of the following paper, which were ported from the now deprecated acccountability implementation provided by the [SAPiC plugin](https://github.com/tamarin-prover/tamarin-prover/tree/be0214d5ea0516f1398744ec44590b5bdff2386a) to the new implementation presented in [1]:
-[2] "Automated Verification of Accountability in Security Protocols", Robert Künnemann, Ilkan Esiyok, and Michael Backes, CSF19.
+### [`previous`](./previous)
+
+This directory contains the case studies of [Künnemann et al. (2019)](https://doi.org/10.1109/CSF.2019.00034), which were ported from the now deprecated accountability implementation provided by the [SAPiC plugin](https://github.com/tamarin-prover/tamarin-prover/tree/be0214d5ea0516f1398744ec44590b5bdff2386a) to the new implementation presented in this paper.
diff --git a/examples/accountability/csf21-acc-unbounded/mixnets/basic/dmn-basic.spthy b/examples/accountability/csf21-acc-unbounded/mixnets/basic/dmn-basic.spthy
index 9982d4b49..e40607238 100644
--- a/examples/accountability/csf21-acc-unbounded/mixnets/basic/dmn-basic.spthy
+++ b/examples/accountability/csf21-acc-unbounded/mixnets/basic/dmn-basic.spthy
@@ -24,7 +24,7 @@ equations:
     adec(sk(x), aenc(pk(x), r, m)) = m
   , adec_suc(sk(x), aenc(pk(x), r, m)) = true
 
-
+heuristic: o "./oracle-dmn-basic"
 
 /*********************************************
 Specification
@@ -215,4 +215,4 @@ analyzed: dmn-basic.spthy
 
 
 
-end
\ No newline at end of file
+end
diff --git a/examples/accountability/csf21-acc-unbounded/mixnets/basic/oracle-dmn-basic b/examples/accountability/csf21-acc-unbounded/mixnets/basic/oracle-dmn-basic
index 1363ea7f0..09e030bce 100755
--- a/examples/accountability/csf21-acc-unbounded/mixnets/basic/oracle-dmn-basic
+++ b/examples/accountability/csf21-acc-unbounded/mixnets/basic/oracle-dmn-basic
@@ -1,4 +1,4 @@
-#!/usr/bin/env python
+#!/usr/bin/env python3
 # -*- coding: utf-8 -*-
 import sys
 
@@ -33,4 +33,4 @@ for current in oracle:
                 break
 
 for num in results:
-    print(num)
\ No newline at end of file
+    print(num)
diff --git a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-1.spthy b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-1.spthy
index 3580f6673..c02ccaeb4 100644
--- a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-1.spthy
+++ b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-1.spthy
@@ -26,6 +26,8 @@ equations:
     adec(sk(x), aenc(pk(x), r, m)) = m
   , adec_suc(sk(x), aenc(pk(x), r, m)) = true
 
+heuristic: o "./oracle-dmn-message-tracing"
+
 
 rule DistinctParty:
     [ ]
@@ -175,4 +177,4 @@ analyzed: dmn-message-tracing-blame-all-1.spthy
 
 
 
-end
\ No newline at end of file
+end
diff --git a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-2.spthy b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-2.spthy
index 2f805b124..67557d6af 100644
--- a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-2.spthy
+++ b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-2.spthy
@@ -26,6 +26,8 @@ equations:
     adec(sk(x), aenc(pk(x), r, m)) = m
   , adec_suc(sk(x), aenc(pk(x), r, m)) = true
 
+heuristic: o "./oracle-dmn-message-tracing"
+
 
 rule DistinctParty:
     [ ]
@@ -184,4 +186,4 @@ analyzed: dmn-message-tracing-blame-all-2.spthy
 
 
 
-end
\ No newline at end of file
+end
diff --git a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-3.spthy b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-3.spthy
index cce57bf2c..48d680c35 100644
--- a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-3.spthy
+++ b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-3.spthy
@@ -26,6 +26,8 @@ equations:
     adec(sk(x), aenc(pk(x), r, m)) = m
   , adec_suc(sk(x), aenc(pk(x), r, m)) = true
 
+heuristic: o "./oracle-dmn-message-tracing"
+
 
 rule DistinctParty:
     [ ]
@@ -193,4 +195,4 @@ analyzed: dmn-message-tracing-blame-all-3.spthy
 
 
 
-end
\ No newline at end of file
+end
diff --git a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-4.spthy b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-4.spthy
index 65ce53122..28f7419e6 100644
--- a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-4.spthy
+++ b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-4.spthy
@@ -26,6 +26,8 @@ equations:
     adec(sk(x), aenc(pk(x), r, m)) = m
   , adec_suc(sk(x), aenc(pk(x), r, m)) = true
 
+heuristic: o "./oracle-dmn-message-tracing"
+
 
 rule DistinctParty:
     [ ]
@@ -202,4 +204,4 @@ analyzed: dmn-message-tracing-blame-all-4.spthy
 
 
 
-end
\ No newline at end of file
+end
diff --git a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-5.spthy b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-5.spthy
index e449b870e..6535963ab 100644
--- a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-5.spthy
+++ b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-all-5.spthy
@@ -26,6 +26,8 @@ equations:
     adec(sk(x), aenc(pk(x), r, m)) = m
   , adec_suc(sk(x), aenc(pk(x), r, m)) = true
 
+heuristic: o "./oracle-dmn-message-tracing"
+
 
 rule DistinctParty:
     [ ]
@@ -211,4 +213,4 @@ analyzed: dmn-message-tracing-blame-all-5.spthy
 
 
 
-end
\ No newline at end of file
+end
diff --git a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-1.spthy b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-1.spthy
index f4ccb005c..6421bb566 100644
--- a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-1.spthy
+++ b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-1.spthy
@@ -26,6 +26,8 @@ equations:
     adec(sk(x), aenc(pk(x), r, m)) = m
   , adec_suc(sk(x), aenc(pk(x), r, m)) = true
 
+heuristic: o "./oracle-dmn-message-tracing"
+
 
 rule DistinctParty:
     [ ]
@@ -164,4 +166,4 @@ analyzed: dmn-message-tracing-blame-first-1.spthy
 
 
 
-end
\ No newline at end of file
+end
diff --git a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-2.spthy b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-2.spthy
index 270fe98de..eb3655617 100644
--- a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-2.spthy
+++ b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-2.spthy
@@ -26,6 +26,8 @@ equations:
     adec(sk(x), aenc(pk(x), r, m)) = m
   , adec_suc(sk(x), aenc(pk(x), r, m)) = true
 
+heuristic: o "./oracle-dmn-message-tracing"
+
 
 rule DistinctParty:
     [ ]
@@ -172,4 +174,4 @@ analyzed: dmn-message-tracing-blame-first-2.spthy
 
 
 
-end
\ No newline at end of file
+end
diff --git a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-3.spthy b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-3.spthy
index a06f7adc3..c6103cba0 100644
--- a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-3.spthy
+++ b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-3.spthy
@@ -26,6 +26,8 @@ equations:
     adec(sk(x), aenc(pk(x), r, m)) = m
   , adec_suc(sk(x), aenc(pk(x), r, m)) = true
 
+heuristic: o "./oracle-dmn-message-tracing"
+
 
 rule DistinctParty:
     [ ]
@@ -180,4 +182,4 @@ analyzed: dmn-message-tracing-blame-first-3.spthy
 
 
 
-end
\ No newline at end of file
+end
diff --git a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-4.spthy b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-4.spthy
index 7e0ea0f6c..4b1e8de24 100644
--- a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-4.spthy
+++ b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-4.spthy
@@ -26,6 +26,8 @@ equations:
     adec(sk(x), aenc(pk(x), r, m)) = m
   , adec_suc(sk(x), aenc(pk(x), r, m)) = true
 
+heuristic: o "./oracle-dmn-message-tracing"
+
 
 rule DistinctParty:
     [ ]
@@ -188,4 +190,4 @@ analyzed: dmn-message-tracing-blame-first-4.spthy
 
 
 
-end
\ No newline at end of file
+end
diff --git a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-5.spthy b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-5.spthy
index 11e725af8..bed8b3d2c 100644
--- a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-5.spthy
+++ b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/dmn-message-tracing-first-5.spthy
@@ -26,6 +26,8 @@ equations:
     adec(sk(x), aenc(pk(x), r, m)) = m
   , adec_suc(sk(x), aenc(pk(x), r, m)) = true
 
+heuristic: o "./oracle-dmn-message-tracing"
+
 
 rule DistinctParty:
     [ ]
@@ -196,4 +198,4 @@ analyzed: dmn-message-tracing-blame-first-5.spthy
 
 
 
-end
\ No newline at end of file
+end
diff --git a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/oracle-dmn-message-tracing b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/oracle-dmn-message-tracing
index a845e23e9..4b4ee8bd9 100755
--- a/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/oracle-dmn-message-tracing
+++ b/examples/accountability/csf21-acc-unbounded/mixnets/message-tracing/oracle-dmn-message-tracing
@@ -1,4 +1,4 @@
-#!/usr/bin/env python
+#!/usr/bin/env python3
 # -*- coding: utf-8 -*-
 import sys
 
@@ -66,4 +66,4 @@ for current in oracle:
                 break
 
 for num in results:
-    print(num)
\ No newline at end of file
+    print(num)
diff --git a/examples/accountability/csf21-acc-unbounded/mixvote/mixvote_SmHh-multi-session.spthy b/examples/accountability/csf21-acc-unbounded/mixvote/mixvote_SmHh-multi-session.spthy
index b39a11f5b..92c07c859 100644
--- a/examples/accountability/csf21-acc-unbounded/mixvote/mixvote_SmHh-multi-session.spthy
+++ b/examples/accountability/csf21-acc-unbounded/mixvote/mixvote_SmHh-multi-session.spthy
@@ -591,4 +591,4 @@ analyzed: mixvote_SmHh-multi-session.spthy
 
 
 
-end
\ No newline at end of file
+end
diff --git a/examples/accountability/csf21-acc-unbounded/previous/ct.spthy b/examples/accountability/csf21-acc-unbounded/previous/ct.spthy
index a48ef4758..cc616142a 100644
--- a/examples/accountability/csf21-acc-unbounded/previous/ct.spthy
+++ b/examples/accountability/csf21-acc-unbounded/previous/ct.spthy
@@ -30,8 +30,7 @@ Specification
 *********************************************/
 
 let CA =
-    let sk = skca($ca) in
-    out(pk(sk));
+    out(pk(skca($ca)));
     // Request to register S at CA
     !(  in(<$s, $ca>);
         new skS;
@@ -39,7 +38,7 @@ let CA =
         // Dishonest CAs cannot register proofs, because they don't have them.
         insert <$ca, 'proofOfID', $s, pk(skS)>, 'yes';
         out(pk(skS));
-        out(sign(sk, <pk(skS), $s>))
+        out(sign(skca($ca), <pk(skS), $s>))
     )
 
 let LogCert =
@@ -65,14 +64,12 @@ let TestCA =
         unlock 'testCA'
 
 let TestLA =
-    let u1 = 'c1' in
-    let u2 = 's1' in
     // This is the test that the AIFom file compiles to, modulo symmetry.
     lock 'log';
-    in(<$la, u1, u2, $s, pk>);
-    lookup <$la, 'log', $s, pk, u1> as x1 in
+    in(<$la, 'c1', 's1', $s, pk>);
+    lookup <$la, 'log', $s, pk, 'c1'> as x1 in
     (
-        lookup <$la, 'log', $s, pk, u2> as x2 in
+        lookup <$la, 'log', $s, pk, 's1'> as x2 in
             event HonestLA();
             event TestLA($la, $s, pk);
             unlock 'log'
@@ -82,7 +79,7 @@ let TestLA =
             unlock 'log'
     )
     else (
-        lookup <$la, 'log', $s, pk, u2> as x2 in
+        lookup <$la, 'log', $s, pk, 's1'> as x2 in
             event DishonestLA($la);
             event TestLA($la, $s, pk);
             unlock 'log'
@@ -97,6 +94,7 @@ let Proto =
     ! in($ca); CA || in($la); LogCert || TestCA || TestLA || Terminate
 
 // General form for accountabilty processes.
+process:
 Proto
 || !( in('c', <'CAcorrupt', $ca>); // corrupt CAs
       event Corrupted($ca);
@@ -201,4 +199,4 @@ analyzed: ct.spthy
 
 
 
-end
\ No newline at end of file
+end
diff --git a/examples/accountability/csf21-acc-unbounded/previous/ocsps-msr.spthy b/examples/accountability/csf21-acc-unbounded/previous/ocsps-msr.spthy
index 41fd9917e..ca7f9db19 100644
--- a/examples/accountability/csf21-acc-unbounded/previous/ocsps-msr.spthy
+++ b/examples/accountability/csf21-acc-unbounded/previous/ocsps-msr.spthy
@@ -176,4 +176,4 @@ analyzed: ocsps-msr.spthy
 
 
 
-end
\ No newline at end of file
+end
diff --git a/examples/accountability/csf21-acc-unbounded/previous/whodunit.spthy b/examples/accountability/csf21-acc-unbounded/previous/whodunit.spthy
index 6f7544b27..57a677088 100644
--- a/examples/accountability/csf21-acc-unbounded/previous/whodunit.spthy
+++ b/examples/accountability/csf21-acc-unbounded/previous/whodunit.spthy
@@ -28,10 +28,9 @@ Specification
 *********************************************/
 
 let S =
-  let m = <<sid, v>, sig(<sid, v>, sk($x))> in
-    in(v);
-    out(c_SA, m);
-    out(c_SJ, m)
+  in(v);
+  out(c_SA, <<sid, v>, sig(<sid, v>, sk($x))>);
+  out(c_SJ, <<sid, v>, sig(<sid, v>, sk($x))>)
 
 let A =
   let pk_x = pk(sk($x)) in
@@ -70,6 +69,7 @@ let P =
     out(pk(sk($y)));
     (S | A | J | !Adv)
 
+process:
 !P
 
 
@@ -118,4 +118,4 @@ analyzed: whodunit.spthy
 
 
 
-end
\ No newline at end of file
+end
diff --git a/examples/accountability/masters-thesis-morio/CentralizedMonitor.spthy b/examples/accountability/masters-thesis-morio/CentralizedMonitor.spthy
index ab1a7e368..f84220a47 100644
--- a/examples/accountability/masters-thesis-morio/CentralizedMonitor.spthy
+++ b/examples/accountability/masters-thesis-morio/CentralizedMonitor.spthy
@@ -31,10 +31,10 @@ predicates:
 let D =
   insert <'roles', $x, 'D'>, true;
   out(pk(sk($x)));
+  in(a);
   let m_1 = <'Do', a>
-    m_2 = <'Permit', a>
+      m_2 = <'Permit', a>
   in
-    in(a);
     if IsNormal(a) then
       out(<m_1, sig(m_1, sk($x))>)
     else if IsSpecial(a) then
@@ -43,37 +43,37 @@ let D =
 let C =
   insert <'roles', $y, 'C'>, true;
   out(pk(sk($y)));
+  in($x);
+  in(<<'Permit', a>, sig_m_2>);
   let m_2 = <'Permit', a>
-    m_3 = <m_2, sig_m_2>
+      m_3 = <m_2, sig_m_2>
   in
-    in($x);
-    in(<m_2, sig_m_2>);
     lookup <'roles', $x, 'D'> as is_d in
       if verify(sig_m_2, m_2, pk(sk($x))) = true then
         if IsSpecial(a) then
           out(<m_3, sig(m_3, sk($y))>)
 
 let M =
-  let m_1 = <'Do', a>
-    m_2 = <'Permit', a>
-    m_3 = <m_2, sig_m_2>
-  in
-  ( in(<m_1, sig_m_1>);
-    if verify(sig_m_1, m_1, pk(sk($x))) = true then
-      lookup <'roles', $x, 'D'> as is_d in
-        new id;
-        event Log($x, a, id);
-        event Execute(a, id)
+  ( in(<<'Do', a>, sig_m_1>);
+    let m_1 = <'Do', a> in
+      if verify(sig_m_1, m_1, pk(sk($x))) = true then
+        lookup <'roles', $x, 'D'> as is_d in
+          new id;
+          event Log($x, a, id);
+          event Execute(a, id)
   )
   +
-  ( in(<m_3, sig_m_3>);
-    if verify(sig_m_3, m_3, pk(sk($y))) = true then
-      if verify(sig_m_2, m_2, pk(sk($x))) = true then
-        lookup <'roles', $y, 'C'> as is_c in
-          lookup <'roles', $x, 'D'> as is_d in
-            new id;
-            event Log(<$x, $y>, a, id);
-            event Execute(a, id)
+  ( in(<<<'Permit', a>, sig_m_2>, sig_m_3>);
+    let m_2 = <'Permit', a>
+        m_3 = <m_2, sig_m_2>
+    in
+      if verify(sig_m_3, m_3, pk(sk($y))) = true then
+        if verify(sig_m_2, m_2, pk(sk($x))) = true then
+          lookup <'roles', $y, 'C'> as is_c in
+            lookup <'roles', $x, 'D'> as is_d in
+              new id;
+              event Log(<$x, $y>, a, id);
+              event Execute(a, id)
   )
 
 let Adv =
@@ -83,8 +83,8 @@ let Adv =
 
 let P = (in($x); D) | (in($y); C) | (in(<$x,$y>); M) | !Adv
 
-
-!P
+process:
+  !P
 
 
 test invalidReqD:
@@ -109,4 +109,4 @@ restriction one_role:
                           ==> #i = #j & r_1 = r_2"
 
 
-end
\ No newline at end of file
+end
diff --git a/examples/accountability/masters-thesis-morio/OCSPS.spthy b/examples/accountability/masters-thesis-morio/OCSPS.spthy
index 67dbabbb1..4e9475ce5 100644
--- a/examples/accountability/masters-thesis-morio/OCSPS.spthy
+++ b/examples/accountability/masters-thesis-morio/OCSPS.spthy
@@ -11,6 +11,15 @@
 theory OCSPS
 begin
 
+heuristic: {rank}
+
+tactic: rank
+prio:
+  regex "Insert|State|Judged|Let"
+prio:
+  regex "KU \( sk|#"
+
+
 functions:
   pk/1, sk/1[private],
   sig/2, verify/3,
@@ -32,17 +41,15 @@ let R =
     lock 'time';
     lookup 'time' as ~t in
       lookup <'cert_status', cert> as status in
-        let resp = <pk(sk($x)), cert, status, ~t> in
-          out(<resp, sig(resp, sk($x))>);
-          unlock 'time'
+        out(<<pk(sk($x)), cert, status, ~t>, sig(<pk(sk($x)), cert, status, ~t>, sk($x))>);
+        unlock 'time'
       else
-        let resp = <pk(sk($x)), cert, 'unkown', ~t> in
-          out(<resp, sig(resp, sk($x))>);
-          unlock 'time'
+        out(<<pk(sk($x)), cert, 'unkown', ~t>, sig(<pk(sk($x)), cert, 'unkown', ~t>, sk($x))>);
+        unlock 'time'
 
 let C =
+  in(<<pk_R, cert, status, ~t>, resp_sig, server_sig>);
   let resp = <pk_R, cert, status, ~t> in
-    in(<resp, resp_sig, server_sig>);
     lookup <'roles', id(pk_R), 'R'> as is_r in
       if verify(resp_sig, resp, pk_R) = true then
         if verify(server_sig, resp, extract(cert)) = true then
@@ -53,9 +60,9 @@ let C =
             event Judged(~t, cert)
 
 let S_h =
-  let resp = <pk_R, c, s, t> in
-    out(cert);
-    in(<resp, resp_sig>);
+  out(cert);
+  in(<<pk_R, c, s, ~t>, resp_sig>);
+  let resp = <pk_R, c, s, ~t> in
     lookup <'roles', id(pk_R), 'R'> as is_r in
       if c = cert then
         if verify(resp_sig, resp, pk_R) = true then
@@ -74,14 +81,12 @@ let S_c =
   unlock 'time'
 
 let S =
-      let cert = sig(pk(sk($x)), sk('CA'))
-          resp = <pk_R, c, s, t>
-      in
-        insert <'roles', $x, 'S'>, true;
-        insert <'cert_status', cert>, 'good';
-        event Secret(cert, sk($x));
-        out(pk(sk($x)));
-        ( S_h + S_c )
+  let cert = sig(pk(sk($x)), sk('CA')) in
+    insert <'roles', $x, 'S'>, true;
+    insert <'cert_status', cert>, 'good';
+    event Secret(cert, sk($x));
+    out(pk(sk($x)));
+    ( S_h + S_c )
 
 let Clock =
   lock 'time';
@@ -100,7 +105,8 @@ let Adv =
 let P = (in($x); R) | C | (in($x); S) | !Clock | !Adv
 
 
-P
+process:
+  P
 
 
 test blamed:
@@ -112,13 +118,11 @@ lemma acc:
                                 Revealed(sk)@k & Time(t)@l & #k < #l)"
 
 
-// restriction R_trusted: // uncomment for untrusted R
-//  "not Ex x #i #j. Corrupted(x)@i & Insert(<'roles', x, 'R'>, true)@j"
+restriction R_trusted: // uncomment for untrusted R
+  "not Ex x #i #j. Corrupted(x)@i & Insert(<'roles', x, 'R'>, true)@j"
 
 restriction one_role:
   "All x r_1 r_2 #i #j. Insert(<'roles', x, r_1>, true)@i &
                         Insert(<'roles', x, r_2>, true)@j
                           ==> #i = #j & r_1 = r_2"
-
-
 end
diff --git a/examples/accountability/masters-thesis-morio/README.md b/examples/accountability/masters-thesis-morio/README.md
new file mode 100644
index 000000000..bcbdc6e42
--- /dev/null
+++ b/examples/accountability/masters-thesis-morio/README.md
@@ -0,0 +1,20 @@
+# Master's Thesis: Verifying Accountability for Unbounded Sets of Participants
+
+This is the artifact for the Master's thesis *Verifying Accountability for Unbounded Sets of Participants* by Kevin Morio.
+
+## Models
+
+```
+.
+├── CentralizedMonitor.spthy
+├── OCSPS-untrusted.spthy
+├── OCSPS.spthy
+└── WhoDunit.spthy
+```
+
+The models were ported from [Künnemann et al. (2019)](https://doi.org/10.1109/CSF.2019.00034) to the new implementation presented in the thesis.
+
+### Changes to the original version
+
+The models have been adapted to the new SAPiC semantic in November 2023.
+The tactic feature is now used for the OCPS models to speed up the verification.
diff --git a/examples/accountability/masters-thesis-morio/WhoDunit.spthy b/examples/accountability/masters-thesis-morio/WhoDunit.spthy
index 2eda644de..124fa0224 100644
--- a/examples/accountability/masters-thesis-morio/WhoDunit.spthy
+++ b/examples/accountability/masters-thesis-morio/WhoDunit.spthy
@@ -21,8 +21,8 @@ equations:
 
 
 let S =
+  in(v);
   let m = <<sid, v>, sig(<sid, v>, sk($x))> in
-    in(v);
     out(c_SA, m);
     out(c_SJ, m)
 
@@ -64,7 +64,8 @@ let P =
     (S | A | J | !Adv)
 
 
-!P
+process:
+  !P
 
 
 test blamed: