# gruninger/colore

Proofs for Allen Interval Algebra theorems

gruninger committed May 15, 2017
1 parent c89628a commit 2913f1f4036ded232601ce279abdf45d0715cf44
 @@ -0,0 +1,64 @@ % Saved by Prover9-Mace4 Version 0.5B, March 2008 (Dec 2007 LADR). set(ignore_option_dependencies). % GUI handles dependencies if(Prover9). % Options for Prover9 assign(max_seconds, 600). end_if. if(Mace4). % Options for Mace4 assign(max_seconds, 60). end_if. formulas(assumptions). %original interval meeting axioms (all i all j all k all m ((meets(i,k) & meets(j,k) & meets(i,m)) -> meets(j,m))). (all i all j all k all l ((meets(i,j) & meets(k,l)) -> (meets(i,l) | b(i,l) | b(k,j)))). (all x all y (pre(x,y) <-> (meets(x,y) | b(x,y) | (x=y)))). (all x all y (b(x,y) <-> (exists z (meets(x,z) & meets(z,y))))). -(all x all y (exists z (pre(x,z) & pre(y,z)))). (all i (exists j exists k (meets(i,j) & meets(k,i)))). (all x all y all z all u ((meets(x,y) & meets(x,z) & meets(y,u) & meets(z,u)) -> (y=z))). end_of_list. formulas(goals). end_of_list.
 @@ -0,0 +1,37 @@ ============================== prooftrans ============================ Prover9 (32) version Dec-2007, Dec 2007. Process 58220 was started by mudcat on Romuald.local, Sat May 6 10:19:28 2017 The command was "/Applications/Prover9-Mace4-v05B.app/Contents/Resources/bin-mac-intel/prover9". ============================== end of head =========================== ============================== end of input ========================== ============================== PROOF ================================= % -------- Comments from original proof -------- % Proof 1 at 0.01 (+ 0.01) seconds. % Length of proof is 17. % Level of proof is 5. % Maximum clause weight is 15. % Given clauses 58. 2 (all i all j all k all l (meets(i,j) & meets(k,l) -> meets(i,l) | b(i,l) | b(k,j))) # label(non_clause). [assumption]. 3 (all x all y (pre(x,y) <-> meets(x,y) | b(x,y) | x = y)) # label(non_clause). [assumption]. 5 -(all x all y exists z (pre(x,z) & pre(y,z))) # label(non_clause). [assumption]. 6 (all i exists j exists k (meets(i,j) & meets(k,i))) # label(non_clause). [assumption]. 9 -meets(x,y) | -meets(z,u) | meets(x,u) | b(x,u) | b(z,y). [clausify(2)]. 11 pre(x,y) | -meets(x,y). [clausify(3)]. 12 pre(x,y) | -b(x,y). [clausify(3)]. 17 -pre(c1,x) | -pre(c2,x). [clausify(5)]. 18 meets(x,f2(x)). [clausify(6)]. 29 pre(x,f2(x)). [resolve(18,a,11,b)]. 31 -meets(x,y) | meets(z,y) | b(z,y) | b(x,f2(z)). [resolve(18,a,9,a)]. 64 -pre(c1,f2(c2)). [resolve(29,a,17,b)]. 65 -pre(c2,f2(c1)). [ur(17,a,29,a)]. 94 -b(c1,f2(c2)). [ur(12,a,64,a)]. 95 -meets(c1,f2(c2)). [ur(11,a,64,a)]. 97 -b(c2,f2(c1)). [ur(12,a,65,a)]. 278 \$F. [ur(31,b,95,a,c,94,a,d,97,a),unit_del(a,18)]. ============================== end of proof ==========================
 @@ -0,0 +1,56 @@ % Saved by Prover9-Mace4 Version 0.5B, March 2008 (Dec 2007 LADR). set(ignore_option_dependencies). % GUI handles dependencies if(Prover9). % Options for Prover9 assign(max_seconds, 600). end_if. if(Mace4). % Options for Mace4 assign(max_seconds, 60). end_if. formulas(assumptions). %original interval meeting axioms (all i all j all k all m ((meets(i,k) & meets(j,k) & meets(i,m)) -> meets(j,m))). (all i all j all k all l ((meets(i,j) & meets(k,l)) -> (meets(i,l) | b(i,l) | b(k,j)))). (all x all y (pre(x,y) <-> (meets(x,y) | b(x,y) | (x=y)))). (all x all y (b(x,y) <-> (exists z (meets(x,z) & meets(z,y))))). -(all x all y (exists z (pre(z,x) & pre(z,y)))). (all i (exists j exists k (meets(i,j) & meets(k,i)))). end_of_list. formulas(goals). end_of_list.
 @@ -0,0 +1,36 @@ ============================== prooftrans ============================ Prover9 (32) version Dec-2007, Dec 2007. Process 50903 was started by mudcat on mie-16-228.internal.mie.utoronto.ca, Mon May 15 14:30:35 2017 The command was "/Applications/Prover9-Mace4-v05B.app/Contents/Resources/bin-mac-intel/prover9". ============================== end of head =========================== ============================== end of input ========================== ============================== PROOF ================================= % -------- Comments from original proof -------- % Proof 1 at 0.01 (+ 0.01) seconds. % Length of proof is 16. % Level of proof is 5. % Maximum clause weight is 15. % Given clauses 53. 2 (all i all j all k all l (meets(i,j) & meets(k,l) -> meets(i,l) | b(i,l) | b(k,j))) # label(non_clause). [assumption]. 3 (all x all y (pre(x,y) <-> meets(x,y) | b(x,y) | x = y)) # label(non_clause). [assumption]. 5 -(all x all y exists z (pre(z,x) & pre(z,y))) # label(non_clause). [assumption]. 6 (all i exists j exists k (meets(i,j) & meets(k,i))) # label(non_clause). [assumption]. 8 -meets(x,y) | -meets(z,u) | meets(x,u) | b(x,u) | b(z,y). [clausify(2)]. 10 pre(x,y) | -meets(x,y). [clausify(3)]. 11 pre(x,y) | -b(x,y). [clausify(3)]. 16 -pre(x,c1) | -pre(x,c2). [clausify(5)]. 18 meets(f3(x),x). [clausify(6)]. 31 pre(f3(x),x). [resolve(18,a,10,b)]. 46 -pre(f3(c2),c1). [resolve(31,a,16,b)]. 47 -pre(f3(c1),c2). [ur(16,a,31,a)]. 74 -b(f3(c2),c1). [ur(11,a,46,a)]. 75 -meets(f3(c2),c1). [ur(10,a,46,a)]. 77 -b(f3(c1),c2). [ur(11,a,47,a)]. 241 \$F. [ur(8,b,18,a,c,75,a,d,74,a,e,77,a),unit_del(a,18)]. ============================== end of proof ==========================
 @@ -0,0 +1,49 @@ formulas(assumptions). -(all i all j all k all m ((meets(i,k) & meets(j,k) & meets(i,m)) -> meets(j,m))). (all i all j all k ((meets(i,j) & meets(j,k)) -> -meets(i,k))). (all i all j all k all l ((meets(i,j) & meets(k,l)) -> (meets(i,l) | (exists n ((meets(i,n) & meets(n,l)) | (meets(k,n) & meets(n,j))))))). (all i all j (meets(i,j) -> -meets(j,i))). (all i all j all k all m ((meets(i,j) & meets(j,k) & meets(k,m)) -> (exists n (meets(i,n) & meets(n,m))))). %unique_interval (all x all y all z all u ((meets(x,y) & meets(x,z) & meets(y,u) & meets(z,u)) -> (y=z))). end_of_list.
 @@ -0,0 +1,66 @@ ============================== prooftrans ============================ Prover9 (32) version Dec-2007, Dec 2007. Process 58801 was started by mudcat on Romuald.local, Sun May 7 11:26:31 2017 The command was "/Applications/Prover9-Mace4-v05B.app/Contents/Resources/bin-mac-intel/prover9". ============================== end of head =========================== ============================== end of input ========================== ============================== PROOF ================================= % -------- Comments from original proof -------- % Proof 1 at 1.63 (+ 0.03) seconds. % Length of proof is 46. % Level of proof is 14. % Maximum clause weight is 41. % Given clauses 606. 1 -(all i all j all k all m (meets(i,k) & meets(j,k) & meets(i,m) -> meets(j,m))) # label(non_clause). [assumption]. 2 (all i all j all k (meets(i,j) & meets(j,k) -> -meets(i,k))) # label(non_clause). [assumption]. 3 (all i all j all k all l (meets(i,j) & meets(k,l) -> meets(i,l) | (exists n (meets(i,n) & meets(n,l) | meets(k,n) & meets(n,j))))) # label(non_clause). [assumption]. 5 (all i all j all k all m (meets(i,j) & meets(j,k) & meets(k,m) -> (exists n (meets(i,n) & meets(n,m))))) # label(non_clause). [assumption]. 7 meets(c1,c3). [clausify(1)]. 8 meets(c2,c3). [clausify(1)]. 9 meets(c1,c4). [clausify(1)]. 10 -meets(c2,c4). [clausify(1)]. 11 -meets(x,y) | -meets(y,z) | -meets(x,z). [clausify(2)]. 12 -meets(x,y) | -meets(z,u) | meets(x,u) | meets(x,f1(x,y,z,u)) | meets(z,f1(x,y,z,u)). [clausify(3)]. 13 -meets(x,y) | -meets(z,u) | meets(x,u) | meets(x,f1(x,y,z,u)) | meets(f1(x,y,z,u),y). [clausify(3)]. 14 -meets(x,y) | -meets(z,u) | meets(x,u) | meets(f1(x,y,z,u),u) | meets(z,f1(x,y,z,u)). [clausify(3)]. 15 -meets(x,y) | -meets(z,u) | meets(x,u) | meets(f1(x,y,z,u),u) | meets(f1(x,y,z,u),y). [clausify(3)]. 17 -meets(x,y) | -meets(y,z) | -meets(z,u) | meets(x,f2(x,y,z,u)). [clausify(5)]. 18 -meets(x,y) | -meets(y,z) | -meets(z,u) | meets(f2(x,y,z,u),u). [clausify(5)]. 27 -meets(c1,x) | -meets(x,c4). [resolve(11,c,9,a)]. 28 -meets(c2,x) | -meets(x,c3). [resolve(11,c,8,a)]. 29 -meets(c1,x) | -meets(x,c3). [resolve(11,c,7,a)]. 35 -meets(x,y) | meets(c2,y) | meets(c2,f1(c2,c3,x,y)) | meets(x,f1(c2,c3,x,y)). [resolve(12,a,8,a)]. 36 -meets(x,y) | meets(c1,y) | meets(c1,f1(c1,c3,x,y)) | meets(x,f1(c1,c3,x,y)). [resolve(12,a,7,a)]. 42 -meets(x,y) | meets(c1,y) | meets(c1,f1(c1,c3,x,y)) | meets(f1(c1,c3,x,y),c3). [resolve(13,a,7,a)]. 47 -meets(x,y) | meets(c2,y) | meets(f1(c2,c3,x,y),y) | meets(x,f1(c2,c3,x,y)). [resolve(14,a,8,a)]. 53 -meets(x,y) | meets(c2,y) | meets(f1(c2,c3,x,y),y) | meets(f1(c2,c3,x,y),c3). [resolve(15,a,8,a)]. 54 -meets(x,y) | meets(c1,y) | meets(f1(c1,c3,x,y),y) | meets(f1(c1,c3,x,y),c3). [resolve(15,a,7,a)]. 89 meets(c2,f1(c2,c3,c1,c4)) | meets(c1,f1(c2,c3,c1,c4)). [resolve(35,a,9,a),unit_del(a,10)]. 100 meets(c1,f1(c2,c3,c1,c4)) | meets(c1,f1(c1,c3,c2,f1(c2,c3,c1,c4))) | meets(c2,f1(c1,c3,c2,f1(c2,c3,c1,c4))). [resolve(89,a,36,a),merge(b)]. 162 meets(c1,f1(c2,c3,c1,c4)) | meets(c1,f1(c1,c3,c2,f1(c2,c3,c1,c4))) | meets(f1(c1,c3,c2,f1(c2,c3,c1,c4)),c3). [resolve(42,a,89,a),merge(d)]. 166 meets(f1(c2,c3,c1,c4),c4) | meets(c1,f1(c2,c3,c1,c4)). [resolve(47,a,9,a),unit_del(a,10)]. 182 meets(c1,f1(c2,c3,c1,c4)) | -meets(x,y) | -meets(y,f1(c2,c3,c1,c4)) | meets(f2(x,y,f1(c2,c3,c1,c4),c4),c4). [resolve(166,a,18,c)]. 185 meets(c1,f1(c2,c3,c1,c4)) | -meets(x,y) | -meets(y,f1(c2,c3,c1,c4)) | meets(x,f2(x,y,f1(c2,c3,c1,c4),c4)). [resolve(166,a,17,c)]. 207 meets(f1(c2,c3,c1,c4),c4) | meets(f1(c2,c3,c1,c4),c3). [resolve(53,a,9,a),unit_del(a,10)]. 227 meets(f1(c2,c3,c1,c4),c3) | -meets(c1,f1(c2,c3,c1,c4)). [resolve(207,a,27,b)]. 253 meets(c1,f1(c2,c3,c1,c4)) | meets(f1(c1,c3,c2,f1(c2,c3,c1,c4)),f1(c2,c3,c1,c4)) | meets(f1(c1,c3,c2,f1(c2,c3,c1,c4)),c3). [resolve(54,a,89,a),merge(d)]. 334 meets(c1,f1(c2,c3,c1,c4)) | meets(c1,f1(c1,c3,c2,f1(c2,c3,c1,c4))) | -meets(f1(c1,c3,c2,f1(c2,c3,c1,c4)),c3). [resolve(100,c,28,a)]. 1038 meets(c1,f1(c2,c3,c1,c4)) | meets(c1,f1(c1,c3,c2,f1(c2,c3,c1,c4))). [resolve(334,c,162,c),merge(c),merge(d)]. 1041 meets(c1,f1(c2,c3,c1,c4)) | -meets(f1(c1,c3,c2,f1(c2,c3,c1,c4)),f1(c2,c3,c1,c4)) | meets(c1,f2(c1,f1(c1,c3,c2,f1(c2,c3,c1,c4)),f1(c2,c3,c1,c4),c4)). [resolve(1038,b,185,b),merge(b)]. 1042 meets(c1,f1(c2,c3,c1,c4)) | -meets(f1(c1,c3,c2,f1(c2,c3,c1,c4)),f1(c2,c3,c1,c4)) | meets(f2(c1,f1(c1,c3,c2,f1(c2,c3,c1,c4)),f1(c2,c3,c1,c4),c4),c4). [resolve(1038,b,182,b),merge(b)]. 1086 meets(c1,f1(c2,c3,c1,c4)) | -meets(f1(c1,c3,c2,f1(c2,c3,c1,c4)),x) | -meets(c1,x). [resolve(1038,b,11,a)]. 4365 meets(c1,f1(c2,c3,c1,c4)) | meets(c1,f2(c1,f1(c1,c3,c2,f1(c2,c3,c1,c4)),f1(c2,c3,c1,c4),c4)) | meets(f1(c1,c3,c2,f1(c2,c3,c1,c4)),c3). [resolve(1041,b,253,b),merge(c)]. 4367 meets(c1,f1(c2,c3,c1,c4)) | meets(c1,f2(c1,f1(c1,c3,c2,f1(c2,c3,c1,c4)),f1(c2,c3,c1,c4),c4)). [resolve(4365,c,1086,b),merge(c),unit_del(c,7)]. 4435 meets(c1,f1(c2,c3,c1,c4)) | -meets(f2(c1,f1(c1,c3,c2,f1(c2,c3,c1,c4)),f1(c2,c3,c1,c4),c4),x) | -meets(c1,x). [resolve(4367,b,11,a)]. 4660 meets(c1,f1(c2,c3,c1,c4)) | meets(f2(c1,f1(c1,c3,c2,f1(c2,c3,c1,c4)),f1(c2,c3,c1,c4),c4),c4) | meets(f1(c1,c3,c2,f1(c2,c3,c1,c4)),c3). [resolve(1042,b,253,b),merge(c)]. 4662 meets(c1,f1(c2,c3,c1,c4)) | meets(f1(c1,c3,c2,f1(c2,c3,c1,c4)),c3). [resolve(4660,b,4435,b),merge(c),unit_del(c,9)]. 4663 meets(c1,f1(c2,c3,c1,c4)). [resolve(4662,b,1086,b),merge(b),unit_del(b,7)]. 4664 meets(f1(c2,c3,c1,c4),c3). [back_unit_del(227),unit_del(b,4663)]. 4674 \$F. [resolve(4663,a,29,a),unit_del(a,4664)]. ============================== end of proof ==========================
 @@ -0,0 +1,39 @@ formulas(assumptions). (all i all j all k all m ((meets(i,k) & meets(j,k) & meets(i,m)) -> meets(j,m))). -(all i all j all k ((meets(i,j) & meets(j,k)) -> -meets(i,k))). (all i all j all k all l ((meets(i,j) & meets(k,l)) -> (meets(i,l) | (exists n ((meets(i,n) & meets(n,l)) | (meets(k,n) & meets(n,j))))))). (all i all j (meets(i,j) -> -meets(j,i))). (all i all j all k all m ((meets(i,j) & meets(j,k) & meets(k,m)) -> (exists n (meets(i,n) & meets(n,m))))). end_of_list.
 @@ -0,0 +1,30 @@ ============================== prooftrans ============================ Prover9 (32) version Dec-2007, Dec 2007. Process 58810 was started by mudcat on Romuald.local, Sun May 7 11:27:24 2017 The command was "/Applications/Prover9-Mace4-v05B.app/Contents/Resources/bin-mac-intel/prover9". ============================== end of head =========================== ============================== end of input ========================== ============================== PROOF ================================= % -------- Comments from original proof -------- % Proof 1 at 0.00 (+ 0.01) seconds. % Length of proof is 10. % Level of proof is 3. % Maximum clause weight is 12. % Given clauses 12. 1 (all i all j all k all m (meets(i,k) & meets(j,k) & meets(i,m) -> meets(j,m))) # label(non_clause). [assumption]. 2 -(all i all j all k (meets(i,j) & meets(j,k) -> -meets(i,k))) # label(non_clause). [assumption]. 4 (all i all j (meets(i,j) -> -meets(j,i))) # label(non_clause). [assumption]. 6 -meets(x,y) | -meets(z,y) | -meets(x,u) | meets(z,u). [clausify(1)]. 7 meets(c1,c2). [clausify(2)]. 8 meets(c2,c3). [clausify(2)]. 9 meets(c1,c3). [clausify(2)]. 14 -meets(x,y) | -meets(y,x). [clausify(4)]. 17 -meets(x,x). [factor(14,a,b)]. 72 \$F. [ur(6,b,8,a,c,7,a,d,17,a),unit_del(a,9)]. ============================== end of proof ==========================