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ex20.out
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ex20.out
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============================== Prover9 ===============================
Prover9 (64) version 2009-11A, November 2009.
Process 6424 was started by qwang on grid01,
Wed Jun 26 22:33:07 2019
The command was "prover9 -f ex20.in".
============================== end of head ===========================
============================== INPUT =================================
% Reading from file ex20.in
formulas(sos).
(all x (sixthstreet(x) & -police(x) -> (exists y (costume(y) & have(x,y))))).
-(exists x (cs(x) & police(x))).
(all x (costume(x) & good(x) -> robot(x))).
(all x (sixthstreet(x) & happy(x) -> (all y (costume(y) & have(x,y) -> good(y))) | drunk(x))).
end_of_list.
formulas(goals).
-(exists x (cs(x) & drunk(x))) & (all y (cs(y) & sixthstreet(y) -> happy(y))) -> (all z (cs(z) & sixthstreet(z) -> (exists u (costume(u) & robot(u) & have(z,u))))).
end_of_list.
============================== end of input ==========================
============================== PROCESS NON-CLAUSAL FORMULAS ==========
% Formulas that are not ordinary clauses:
1 (all x (sixthstreet(x) & -police(x) -> (exists y (costume(y) & have(x,y))))) # label(non_clause). [assumption].
2 -(exists x (cs(x) & police(x))) # label(non_clause). [assumption].
3 (all x (costume(x) & good(x) -> robot(x))) # label(non_clause). [assumption].
4 (all x (sixthstreet(x) & happy(x) -> (all y (costume(y) & have(x,y) -> good(y))) | drunk(x))) # label(non_clause). [assumption].
5 -(exists x (cs(x) & drunk(x))) & (all y (cs(y) & sixthstreet(y) -> happy(y))) -> (all z (cs(z) & sixthstreet(z) -> (exists u (costume(u) & robot(u) & have(z,u))))) # label(non_clause) # label(goal). [goal].
============================== end of process non-clausal formulas ===
============================== PROCESS INITIAL CLAUSES ===============
% Clauses before input processing:
formulas(usable).
end_of_list.
formulas(sos).
-sixthstreet(x) | police(x) | costume(f1(x)). [clausify(1)].
-sixthstreet(x) | police(x) | have(x,f1(x)). [clausify(1)].
-cs(x) | -police(x). [clausify(2)].
-costume(x) | -good(x) | robot(x). [clausify(3)].
-sixthstreet(x) | -happy(x) | -costume(y) | -have(x,y) | good(y) | drunk(x). [clausify(4)].
-cs(x) | -drunk(x). [deny(5)].
-cs(x) | -sixthstreet(x) | happy(x). [deny(5)].
cs(c1). [deny(5)].
sixthstreet(c1). [deny(5)].
-costume(x) | -robot(x) | -have(c1,x). [deny(5)].
end_of_list.
formulas(demodulators).
end_of_list.
============================== PREDICATE ELIMINATION =================
Eliminating sixthstreet/1
6 sixthstreet(c1). [deny(5)].
7 -sixthstreet(x) | police(x) | costume(f1(x)). [clausify(1)].
8 -sixthstreet(x) | police(x) | have(x,f1(x)). [clausify(1)].
9 -sixthstreet(x) | -happy(x) | -costume(y) | -have(x,y) | good(y) | drunk(x). [clausify(4)].
10 -cs(x) | -sixthstreet(x) | happy(x). [deny(5)].
Derived: police(c1) | costume(f1(c1)). [resolve(6,a,7,a)].
Derived: police(c1) | have(c1,f1(c1)). [resolve(6,a,8,a)].
Derived: -happy(c1) | -costume(x) | -have(c1,x) | good(x) | drunk(c1). [resolve(6,a,9,a)].
Derived: -cs(c1) | happy(c1). [resolve(6,a,10,b)].
Eliminating cs/1
11 cs(c1). [deny(5)].
12 -cs(x) | -police(x). [clausify(2)].
13 -cs(x) | -drunk(x). [deny(5)].
Derived: -police(c1). [resolve(11,a,12,a)].
Derived: -drunk(c1). [resolve(11,a,13,a)].
14 -cs(c1) | happy(c1). [resolve(6,a,10,b)].
Derived: happy(c1). [resolve(14,a,11,a)].
Eliminating costume/1
15 police(c1) | costume(f1(c1)). [resolve(6,a,7,a)].
16 -costume(x) | -good(x) | robot(x). [clausify(3)].
17 -costume(x) | -robot(x) | -have(c1,x). [deny(5)].
Derived: police(c1) | -good(f1(c1)) | robot(f1(c1)). [resolve(15,b,16,a)].
Derived: police(c1) | -robot(f1(c1)) | -have(c1,f1(c1)). [resolve(15,b,17,a)].
18 -happy(c1) | -costume(x) | -have(c1,x) | good(x) | drunk(c1). [resolve(6,a,9,a)].
Derived: -happy(c1) | -have(c1,f1(c1)) | good(f1(c1)) | drunk(c1) | police(c1). [resolve(18,b,15,b)].
Eliminating police/1
19 -police(c1). [resolve(11,a,12,a)].
20 police(c1) | have(c1,f1(c1)). [resolve(6,a,8,a)].
Derived: have(c1,f1(c1)). [resolve(19,a,20,a)].
21 police(c1) | -good(f1(c1)) | robot(f1(c1)). [resolve(15,b,16,a)].
Derived: -good(f1(c1)) | robot(f1(c1)). [resolve(21,a,19,a)].
22 police(c1) | -robot(f1(c1)) | -have(c1,f1(c1)). [resolve(15,b,17,a)].
Derived: -robot(f1(c1)) | -have(c1,f1(c1)). [resolve(22,a,19,a)].
23 -happy(c1) | -have(c1,f1(c1)) | good(f1(c1)) | drunk(c1) | police(c1). [resolve(18,b,15,b)].
Derived: -happy(c1) | -have(c1,f1(c1)) | good(f1(c1)) | drunk(c1). [resolve(23,e,19,a)].
Eliminating drunk/1
24 -happy(c1) | -have(c1,f1(c1)) | good(f1(c1)) | drunk(c1). [resolve(23,e,19,a)].
25 -drunk(c1). [resolve(11,a,13,a)].
Derived: -happy(c1) | -have(c1,f1(c1)) | good(f1(c1)). [resolve(24,d,25,a)].
Eliminating happy/1
26 -happy(c1) | -have(c1,f1(c1)) | good(f1(c1)). [resolve(24,d,25,a)].
27 happy(c1). [resolve(14,a,11,a)].
Derived: -have(c1,f1(c1)) | good(f1(c1)). [resolve(26,a,27,a)].
Eliminating have/2
28 -robot(f1(c1)) | -have(c1,f1(c1)). [resolve(22,a,19,a)].
29 have(c1,f1(c1)). [resolve(19,a,20,a)].
Derived: -robot(f1(c1)). [resolve(28,b,29,a)].
30 -have(c1,f1(c1)) | good(f1(c1)). [resolve(26,a,27,a)].
Derived: good(f1(c1)). [resolve(30,a,29,a)].
Eliminating good/1
31 good(f1(c1)). [resolve(30,a,29,a)].
32 -good(f1(c1)) | robot(f1(c1)). [resolve(21,a,19,a)].
Derived: robot(f1(c1)). [resolve(31,a,32,a)].
Eliminating robot/1
33 robot(f1(c1)). [resolve(31,a,32,a)].
34 -robot(f1(c1)). [resolve(28,b,29,a)].
Derived: $F. [resolve(33,a,34,a)].
============================== end predicate elimination =============
Auto_denials: (no changes).
Term ordering decisions:
Predicate symbol precedence: predicate_order([ ]).
Function symbol precedence: function_order([ ]).
After inverse_order: (no changes).
Unfolding symbols: (none).
Auto_inference settings:
% set(neg_binary_resolution). % (HNE depth_diff=0)
% clear(ordered_res). % (HNE depth_diff=0)
% set(ur_resolution). % (HNE depth_diff=0)
% set(ur_resolution) -> set(pos_ur_resolution).
% set(ur_resolution) -> set(neg_ur_resolution).
Auto_process settings: (no changes).
============================== PROOF =================================
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 35.
% Level of proof is 9.
% Maximum clause weight is 0.000.
% Given clauses 0.
1 (all x (sixthstreet(x) & -police(x) -> (exists y (costume(y) & have(x,y))))) # label(non_clause). [assumption].
2 -(exists x (cs(x) & police(x))) # label(non_clause). [assumption].
3 (all x (costume(x) & good(x) -> robot(x))) # label(non_clause). [assumption].
4 (all x (sixthstreet(x) & happy(x) -> (all y (costume(y) & have(x,y) -> good(y))) | drunk(x))) # label(non_clause). [assumption].
5 -(exists x (cs(x) & drunk(x))) & (all y (cs(y) & sixthstreet(y) -> happy(y))) -> (all z (cs(z) & sixthstreet(z) -> (exists u (costume(u) & robot(u) & have(z,u))))) # label(non_clause) # label(goal). [goal].
6 sixthstreet(c1). [deny(5)].
7 -sixthstreet(x) | police(x) | costume(f1(x)). [clausify(1)].
8 -sixthstreet(x) | police(x) | have(x,f1(x)). [clausify(1)].
9 -sixthstreet(x) | -happy(x) | -costume(y) | -have(x,y) | good(y) | drunk(x). [clausify(4)].
10 -cs(x) | -sixthstreet(x) | happy(x). [deny(5)].
11 cs(c1). [deny(5)].
12 -cs(x) | -police(x). [clausify(2)].
13 -cs(x) | -drunk(x). [deny(5)].
14 -cs(c1) | happy(c1). [resolve(6,a,10,b)].
15 police(c1) | costume(f1(c1)). [resolve(6,a,7,a)].
16 -costume(x) | -good(x) | robot(x). [clausify(3)].
17 -costume(x) | -robot(x) | -have(c1,x). [deny(5)].
18 -happy(c1) | -costume(x) | -have(c1,x) | good(x) | drunk(c1). [resolve(6,a,9,a)].
19 -police(c1). [resolve(11,a,12,a)].
20 police(c1) | have(c1,f1(c1)). [resolve(6,a,8,a)].
21 police(c1) | -good(f1(c1)) | robot(f1(c1)). [resolve(15,b,16,a)].
22 police(c1) | -robot(f1(c1)) | -have(c1,f1(c1)). [resolve(15,b,17,a)].
23 -happy(c1) | -have(c1,f1(c1)) | good(f1(c1)) | drunk(c1) | police(c1). [resolve(18,b,15,b)].
24 -happy(c1) | -have(c1,f1(c1)) | good(f1(c1)) | drunk(c1). [resolve(23,e,19,a)].
25 -drunk(c1). [resolve(11,a,13,a)].
26 -happy(c1) | -have(c1,f1(c1)) | good(f1(c1)). [resolve(24,d,25,a)].
27 happy(c1). [resolve(14,a,11,a)].
28 -robot(f1(c1)) | -have(c1,f1(c1)). [resolve(22,a,19,a)].
29 have(c1,f1(c1)). [resolve(19,a,20,a)].
30 -have(c1,f1(c1)) | good(f1(c1)). [resolve(26,a,27,a)].
31 good(f1(c1)). [resolve(30,a,29,a)].
32 -good(f1(c1)) | robot(f1(c1)). [resolve(21,a,19,a)].
33 robot(f1(c1)). [resolve(31,a,32,a)].
34 -robot(f1(c1)). [resolve(28,b,29,a)].
35 $F. [resolve(33,a,34,a)].
============================== end of proof ==========================
============================== STATISTICS ============================
Given=0. Generated=1. Kept=0. proofs=1.
Usable=0. Sos=0. Demods=0. Limbo=0, Disabled=30. Hints=0.
Kept_by_rule=0, Deleted_by_rule=0.
Forward_subsumed=0. Back_subsumed=0.
Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0.
Demod_attempts=0. Demod_rewrites=0.
Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0.
Megabytes=0.05.
User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
============================== end of statistics =====================
============================== end of search =========================
THEOREM PROVED
Exiting with 1 proof.
Process 6424 exit (max_proofs) Wed Jun 26 22:33:07 2019