TSTP Solution File: GRP401-1 by SNARK---20120808r022
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP401-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:38:06 EDT 2022
% Result : Unsatisfiable 6.22s 6.41s
% Output : Refutation 6.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 6
% Syntax : Number of clauses : 113 ( 96 unt; 0 nHn; 22 RR)
% Number of literals : 130 ( 129 equ; 23 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 285 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_of_multiply,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP008-0.ax',associativity_of_multiply) ).
cnf(right_cancellation,axiom,
( multiply(X,Y) != multiply(Z,Y)
| X = Z ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP008-1.ax',right_cancellation) ).
cnf(left_cancellation,axiom,
( multiply(X,Y) != multiply(X,Z)
| Y = Z ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP008-1.ax',left_cancellation) ).
cnf(commutator,axiom,
multiply(X,Y) = multiply(Y,multiply(X,commutator(X,Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator) ).
cnf(5,plain,
multiply(X,Y) = multiply(multiply(Y,X),commutator(X,Y)),
inference('REWRITE',[status(thm)],[commutator,associativity_of_multiply,theory(equality)]) ).
cnf(commutator_distributes_over_product,axiom,
commutator(multiply(X,Y),Z) = multiply(commutator(X,Z),commutator(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator_distributes_over_product) ).
cnf(prove_nilpotency,negated_conjecture,
multiply(commutator(a,b),c) != multiply(c,commutator(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_nilpotency) ).
cnf(8,plain,
( multiply(X,multiply(Y,Z)) != multiply(multiply(X,Y),U)
| Z = U ),
inference('PARAMODULATE',[status(thm)],[left_cancellation,associativity_of_multiply,theory(equality)]) ).
cnf(9,plain,
( multiply(multiply(X,Y),Z) != multiply(U,multiply(Y,Z))
| X = U ),
inference('PARAMODULATE',[status(thm)],[right_cancellation,associativity_of_multiply,theory(equality)]) ).
cnf(10,plain,
( multiply(X,multiply(Y,Z)) != multiply(U,Z)
| multiply(X,Y) = U ),
inference('PARAMODULATE',[status(thm)],[right_cancellation,associativity_of_multiply,theory(equality)]) ).
cnf(11,plain,
multiply(multiply(X,multiply(Y,Z)),U) = multiply(multiply(X,Y),multiply(Z,U)),
inference('PARAMODULATE',[status(thm)],[associativity_of_multiply,associativity_of_multiply,theory(equality)]) ).
cnf(13,plain,
multiply(multiply(multiply(X,Y),Z),U) = multiply(X,multiply(Y,multiply(Z,U))),
inference('PARAMODULATE',[status(thm)],[associativity_of_multiply,associativity_of_multiply,theory(equality)]) ).
cnf(14,plain,
( multiply(multiply(X,Y),Z) != multiply(X,U)
| multiply(Y,Z) = U ),
inference('PARAMODULATE',[status(thm)],[left_cancellation,associativity_of_multiply,theory(equality)]) ).
cnf(15,plain,
multiply(multiply(multiply(X,Y),Z),U) = multiply(X,multiply(multiply(Y,Z),U)),
inference('PARAMODULATE',[status(thm)],[associativity_of_multiply,associativity_of_multiply,theory(equality)]) ).
cnf(16,plain,
multiply(multiply(X,Y),multiply(Z,U)) = multiply(X,multiply(multiply(Y,Z),U)),
inference('PARAMODULATE',[status(thm)],[associativity_of_multiply,associativity_of_multiply,theory(equality)]) ).
cnf(18,plain,
( multiply(X,Y) != multiply(Z,commutator(X,Y))
| multiply(Y,X) = Z ),
inference('PARAMODULATE',[status(thm)],[right_cancellation,5,theory(equality)]) ).
cnf(19,plain,
multiply(multiply(X,Y),Z) = multiply(multiply(Y,X),multiply(commutator(X,Y),Z)),
inference('PARAMODULATE',[status(thm)],[associativity_of_multiply,5,theory(equality)]) ).
cnf(20,plain,
multiply(multiply(X,Y),multiply(Z,commutator(Z,Y))) = multiply(X,multiply(Z,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity_of_multiply,5,theory(equality)]),11,theory(equality)]) ).
cnf(22,plain,
multiply(multiply(X,Y),Z) = multiply(multiply(multiply(Z,X),Y),commutator(multiply(X,Y),Z)),
inference('PARAMODULATE',[status(thm)],[5,associativity_of_multiply,theory(equality)]) ).
cnf(23,plain,
multiply(commutator(X,Y),multiply(Y,X)) = multiply(multiply(X,Y),commutator(commutator(X,Y),multiply(Y,X))),
inference('PARAMODULATE',[status(thm)],[5,5,theory(equality)]) ).
cnf(25,plain,
multiply(X,multiply(commutator(a,b),c)) != multiply(X,multiply(c,commutator(a,b))),
inference('UR-RESOLVE',[status(thm)],[left_cancellation,prove_nilpotency]) ).
cnf(28,plain,
multiply(commutator(multiply(X,Y),Z),U) = multiply(commutator(X,Z),multiply(commutator(Y,Z),U)),
inference('PARAMODULATE',[status(thm)],[associativity_of_multiply,commutator_distributes_over_product,theory(equality)]) ).
cnf(29,plain,
multiply(multiply(X,commutator(Y,Z)),commutator(U,Z)) = multiply(X,commutator(multiply(Y,U),Z)),
inference('PARAMODULATE',[status(thm)],[associativity_of_multiply,commutator_distributes_over_product,theory(equality)]) ).
cnf(32,plain,
( multiply(X,multiply(Y,Z)) != multiply(Y,X)
| Z = commutator(Y,X) ),
inference('PARAMODULATE',[status(thm)],[8,5,theory(equality)]) ).
cnf(45,plain,
( multiply(X,Y) != multiply(Z,multiply(X,commutator(X,Y)))
| Y = Z ),
inference('PARAMODULATE',[status(thm)],[9,5,theory(equality)]) ).
cnf(89,plain,
multiply(multiply(X,commutator(multiply(Y,Z),U)),V) = multiply(multiply(X,commutator(Y,U)),multiply(commutator(Z,U),V)),
inference('PARAMODULATE',[status(thm)],[11,commutator_distributes_over_product,theory(equality)]) ).
cnf(242,plain,
multiply(X,commutator(X,X)) = X,
inference('HYPERRESOLVE',[status(thm)],[14,5]) ).
cnf(245,plain,
( multiply(X,Y) != multiply(Y,Z)
| multiply(X,commutator(X,Y)) = Z ),
inference('PARAMODULATE',[status(thm)],[14,5,theory(equality)]) ).
cnf(268,plain,
( X != multiply(X,Y)
| commutator(X,X) = Y ),
inference('PARAMODULATE',[status(thm)],[left_cancellation,242,theory(equality)]) ).
cnf(272,plain,
multiply(X,Y) = multiply(X,multiply(commutator(X,X),Y)),
inference('PARAMODULATE',[status(thm)],[associativity_of_multiply,242,theory(equality)]) ).
cnf(273,plain,
multiply(commutator(X,X),X) = multiply(X,commutator(commutator(X,X),X)),
inference('PARAMODULATE',[status(thm)],[5,242,theory(equality)]) ).
cnf(318,plain,
X = multiply(commutator(Y,Y),X),
inference('HYPERRESOLVE',[status(thm)],[left_cancellation,272]) ).
cnf(320,plain,
X = multiply(X,commutator(commutator(X,X),X)),
inference('REWRITE',[status(thm)],[273,318,theory(equality)]) ).
cnf(321,plain,
commutator(multiply(X,Y),X) = commutator(Y,X),
inference('PARAMODULATE',[status(thm)],[commutator_distributes_over_product,318,theory(equality)]) ).
cnf(323,plain,
( X != multiply(Y,X)
| commutator(Z,Z) = Y ),
inference('PARAMODULATE',[status(thm)],[right_cancellation,318,theory(equality)]) ).
cnf(332,plain,
commutator(X,X) = commutator(commutator(X,X),X),
inference('HYPERRESOLVE',[status(thm)],[268,320]) ).
cnf(333,plain,
commutator(multiply(X,commutator(Y,Y)),Y) = commutator(multiply(X,Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[commutator_distributes_over_product,332,theory(equality)]),commutator_distributes_over_product,theory(equality)]) ).
cnf(335,plain,
commutator(multiply(X,Y),multiply(Y,X)) = commutator(commutator(X,Y),multiply(Y,X)),
inference('PARAMODULATE',[status(thm)],[321,5,theory(equality)]) ).
cnf(351,plain,
commutator(X,X) = commutator(Y,Y),
inference('HYPERRESOLVE',[status(thm)],[323,318]) ).
cnf(361,plain,
multiply(X,commutator(Y,Y)) = X,
inference('PARAMODULATE',[status(thm)],[242,351,theory(equality)]) ).
cnf(364,plain,
commutator(X,Y) = commutator(multiply(X,Y),Y),
inference('REWRITE',[status(thm)],[333,361,theory(equality)]) ).
cnf(368,plain,
( X != multiply(X,Y)
| commutator(Z,Z) = Y ),
inference('PARAMODULATE',[status(thm)],[left_cancellation,361,theory(equality)]) ).
cnf(373,plain,
commutator(multiply(X,Y),commutator(Y,X)) = commutator(multiply(Y,X),commutator(Y,X)),
inference('PARAMODULATE',[status(thm)],[364,5,theory(equality)]) ).
cnf(422,plain,
multiply(multiply(multiply(X,Y),Z),commutator(Z,Y)) = multiply(X,multiply(Z,Y)),
inference('PARAMODULATE',[status(thm)],[15,5,theory(equality)]) ).
cnf(690,plain,
multiply(multiply(commutator(X,Y),Z),multiply(Y,X)) = multiply(multiply(multiply(X,Y),Z),commutator(multiply(commutator(X,Y),Z),multiply(Y,X))),
inference('PARAMODULATE',[status(thm)],[5,19,theory(equality)]) ).
cnf(706,plain,
multiply(multiply(X,Y),commutator(commutator(X,Y),X)) = multiply(Y,multiply(commutator(X,Y),X)),
inference('PARAMODULATE',[status(thm)],[19,20,theory(equality)]) ).
cnf(787,plain,
multiply(multiply(a,b),c) != multiply(multiply(b,a),multiply(c,commutator(a,b))),
inference('PARAMODULATE',[status(thm)],[25,19,theory(equality)]) ).
cnf(848,plain,
commutator(X,Y) = commutator(X,multiply(X,Y)),
inference('HYPERRESOLVE',[status(thm)],[32,20]) ).
cnf(884,plain,
commutator(X,multiply(Y,Z)) = commutator(X,multiply(multiply(X,Y),Z)),
inference('PARAMODULATE',[status(thm)],[848,associativity_of_multiply,theory(equality)]) ).
cnf(885,plain,
commutator(multiply(X,Y),commutator(Y,X)) = commutator(commutator(X,Y),multiply(Y,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[848,5,theory(equality)]),335,theory(equality)]) ).
cnf(912,plain,
( multiply(X,Y) != multiply(Z,multiply(multiply(Y,X),commutator(multiply(Y,X),commutator(X,Y))))
| commutator(X,Y) = Z ),
inference('PARAMODULATE',[status(thm)],[45,5,theory(equality)]) ).
cnf(1371,plain,
multiply(multiply(c,commutator(a,b)),multiply(b,a)) != multiply(multiply(multiply(a,b),c),commutator(multiply(c,commutator(a,b)),multiply(b,a))),
inference('UR-RESOLVE',[status(thm)],[18,787]) ).
cnf(1423,plain,
commutator(X,multiply(Y,commutator(Y,X))) = commutator(X,multiply(Y,X)),
inference('PARAMODULATE',[status(thm)],[884,5,theory(equality)]) ).
cnf(1528,plain,
multiply(multiply(X,commutator(X,Y)),Y) = multiply(multiply(X,Y),commutator(multiply(X,commutator(X,Y)),Y)),
inference('PARAMODULATE',[status(thm)],[22,5,theory(equality)]) ).
cnf(1700,plain,
multiply(commutator(multiply(X,Y),multiply(X,Z)),U) = multiply(commutator(X,Z),multiply(commutator(Y,multiply(X,Z)),U)),
inference('PARAMODULATE',[status(thm)],[28,848,theory(equality)]) ).
cnf(1849,plain,
multiply(commutator(X,Y),Y) = multiply(Y,commutator(multiply(X,commutator(X,Y)),Y)),
inference('PARAMODULATE',[status(thm)],[5,29,theory(equality)]) ).
cnf(2058,plain,
multiply(commutator(X,Y),multiply(Y,X)) = multiply(multiply(X,Y),commutator(multiply(X,Y),commutator(Y,X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[5,885,theory(equality)]),5,theory(equality)]) ).
cnf(2059,plain,
( multiply(X,Y) != multiply(Z,multiply(commutator(Y,X),multiply(X,Y)))
| commutator(X,Y) = Z ),
inference('REWRITE',[status(thm)],[912,2058,theory(equality)]) ).
cnf(2062,plain,
commutator(multiply(X,commutator(Y,Z)),multiply(Z,Y)) = multiply(commutator(X,multiply(Z,Y)),commutator(multiply(Y,Z),commutator(Z,Y))),
inference('PARAMODULATE',[status(thm)],[commutator_distributes_over_product,885,theory(equality)]) ).
cnf(2068,plain,
multiply(X,commutator(multiply(Y,Z),commutator(Z,Y))) = multiply(X,commutator(commutator(Y,Z),multiply(Z,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[29,885,theory(equality)]),29,theory(equality)]) ).
cnf(2078,plain,
multiply(multiply(X,commutator(Y,Z)),multiply(commutator(Z,Y),multiply(Y,Z))) = multiply(X,multiply(Y,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[422,885,theory(equality)]),5,23,16,11,theory(equality)]) ).
cnf(2083,plain,
multiply(multiply(X,commutator(multiply(Y,Z),commutator(Z,Y))),commutator(U,multiply(Z,Y))) = multiply(X,commutator(multiply(commutator(Y,Z),U),multiply(Z,Y))),
inference('PARAMODULATE',[status(thm)],[29,885,theory(equality)]) ).
cnf(2235,plain,
commutator(commutator(X,Y),multiply(commutator(Y,X),multiply(X,Y))) = commutator(commutator(X,Y),multiply(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1423,885,theory(equality)]),5,23,theory(equality)]) ).
cnf(2243,plain,
commutator(multiply(multiply(X,commutator(X,Y)),Y),commutator(Y,multiply(X,Y))) = commutator(commutator(multiply(X,commutator(X,Y)),Y),multiply(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[885,1423,theory(equality)]),5,associativity_of_multiply,theory(equality)]) ).
cnf(2248,plain,
multiply(commutator(X,Y),Y) = multiply(Y,commutator(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1849,321,theory(equality)]),364,5,theory(equality)]) ).
cnf(2326,plain,
multiply(X,commutator(X,commutator(Y,X))) = X,
inference('HYPERRESOLVE',[status(thm)],[245,2248]) ).
cnf(2329,plain,
commutator(multiply(X,commutator(X,Y)),Y) = commutator(X,Y),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[245,2248]),commutator_distributes_over_product,theory(equality)]) ).
cnf(2364,plain,
multiply(multiply(X,commutator(X,Y)),Y) = multiply(multiply(X,Y),commutator(X,Y)),
inference('REWRITE',[status(thm)],[1528,2329,theory(equality)]) ).
cnf(2368,plain,
commutator(multiply(multiply(X,Y),commutator(X,Y)),commutator(Y,multiply(X,Y))) = commutator(commutator(X,Y),multiply(X,Y)),
inference('REWRITE',[status(thm)],[2243,2364,2329,theory(equality)]) ).
cnf(2402,plain,
multiply(multiply(X,commutator(Y,X)),Z) = multiply(commutator(Y,X),multiply(X,Z)),
inference('PARAMODULATE',[status(thm)],[associativity_of_multiply,2248,theory(equality)]) ).
cnf(2499,plain,
commutator(X,X) = commutator(Y,commutator(Z,Y)),
inference('HYPERRESOLVE',[status(thm)],[368,2326]) ).
cnf(2889,plain,
commutator(X,X) = commutator(multiply(Y,Z),commutator(Y,Z)),
inference('PARAMODULATE',[status(thm)],[2499,848,theory(equality)]) ).
cnf(2904,plain,
commutator(multiply(X,Y),commutator(Z,X)) = commutator(Y,commutator(Z,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[commutator_distributes_over_product,2499,theory(equality)]),318,theory(equality)]) ).
cnf(2910,plain,
commutator(commutator(X,Y),commutator(Y,multiply(X,Y))) = commutator(commutator(X,Y),multiply(X,Y)),
inference('REWRITE',[status(thm)],[2368,2904,theory(equality)]) ).
cnf(2956,plain,
commutator(multiply(X,commutator(Y,Z)),multiply(Z,Y)) = multiply(commutator(X,multiply(Z,Y)),commutator(Z,commutator(Z,Y))),
inference('REWRITE',[status(thm)],[2062,2904,theory(equality)]) ).
cnf(2957,plain,
multiply(X,commutator(Y,commutator(Y,Z))) = multiply(X,commutator(commutator(Z,Y),multiply(Y,Z))),
inference('REWRITE',[status(thm)],[2068,2904,theory(equality)]) ).
cnf(2968,plain,
multiply(commutator(X,Y),multiply(Y,X)) = multiply(multiply(X,Y),commutator(Y,commutator(Y,X))),
inference('REWRITE',[status(thm)],[23,2957,theory(equality)]) ).
cnf(2969,plain,
multiply(multiply(X,commutator(Y,commutator(Y,Z))),commutator(U,multiply(Y,Z))) = multiply(X,commutator(multiply(commutator(Z,Y),U),multiply(Y,Z))),
inference('REWRITE',[status(thm)],[2083,2904,theory(equality)]) ).
cnf(2982,plain,
commutator(X,commutator(X,Y)) = commutator(multiply(X,Y),commutator(X,Y)),
inference('REWRITE',[status(thm)],[373,2904,theory(equality)]) ).
cnf(3009,plain,
commutator(X,X) = commutator(Y,commutator(Y,Z)),
inference('REWRITE',[status(thm)],[2889,2982,theory(equality)]) ).
cnf(3027,plain,
commutator(X,commutator(X,Y)) = commutator(commutator(Y,X),multiply(X,Y)),
inference('REWRITE',[status(thm)],[885,2904,theory(equality)]) ).
cnf(3375,plain,
multiply(commutator(multiply(X,Y),Z),multiply(Z,multiply(X,Y))) = multiply(multiply(X,multiply(Y,Z)),commutator(Z,commutator(Z,multiply(X,Y)))),
inference('PARAMODULATE',[status(thm)],[2968,associativity_of_multiply,theory(equality)]) ).
cnf(3455,plain,
multiply(commutator(multiply(X,Y),commutator(Y,commutator(Y,X))),multiply(commutator(Y,commutator(Y,X)),multiply(X,Y))) = multiply(multiply(commutator(X,Y),multiply(Y,X)),commutator(commutator(Y,commutator(Y,X)),commutator(commutator(Y,commutator(Y,X)),multiply(X,Y)))),
inference('PARAMODULATE',[status(thm)],[2968,2968,theory(equality)]) ).
cnf(3459,plain,
multiply(X,commutator(Y,commutator(Y,Z))) = X,
inference('PARAMODULATE',[status(thm)],[361,3009,theory(equality)]) ).
cnf(3464,plain,
multiply(commutator(multiply(X,Y),commutator(Y,commutator(Y,X))),multiply(commutator(Y,commutator(Y,X)),multiply(X,Y))) = multiply(commutator(X,Y),multiply(Y,X)),
inference('REWRITE',[status(thm)],[3455,3459,theory(equality)]) ).
cnf(3473,plain,
multiply(commutator(multiply(X,Y),Z),multiply(Z,multiply(X,Y))) = multiply(X,multiply(Y,Z)),
inference('REWRITE',[status(thm)],[3375,3459,theory(equality)]) ).
cnf(3474,plain,
multiply(X,Y) = multiply(commutator(X,Y),multiply(Y,X)),
inference('REWRITE',[status(thm)],[3464,3459,3473,theory(equality)]) ).
cnf(3484,plain,
multiply(multiply(X,commutator(Y,Z)),multiply(Z,Y)) = multiply(X,multiply(Y,Z)),
inference('REWRITE',[status(thm)],[2078,3474,theory(equality)]) ).
cnf(3486,plain,
multiply(c,multiply(a,b)) != multiply(multiply(multiply(a,b),c),commutator(multiply(c,commutator(a,b)),multiply(b,a))),
inference('REWRITE',[status(thm)],[1371,3484,theory(equality)]) ).
cnf(3488,plain,
( multiply(X,Y) != multiply(Z,multiply(Y,X))
| commutator(X,Y) = Z ),
inference('REWRITE',[status(thm)],[2059,3474,theory(equality)]) ).
cnf(3490,plain,
commutator(X,commutator(X,Y)) = commutator(commutator(Y,X),multiply(Y,X)),
inference('REWRITE',[status(thm)],[2235,3027,3474,theory(equality)]) ).
cnf(3492,plain,
commutator(commutator(X,Y),commutator(Y,multiply(X,Y))) = commutator(Y,commutator(Y,X)),
inference('REWRITE',[status(thm)],[2910,3490,theory(equality)]) ).
cnf(3546,plain,
multiply(X,commutator(Y,multiply(Z,U))) = multiply(X,commutator(multiply(commutator(U,Z),Y),multiply(Z,U))),
inference('REWRITE',[status(thm)],[2969,3459,theory(equality)]) ).
cnf(3547,plain,
multiply(multiply(commutator(X,Y),Z),multiply(Y,X)) = multiply(multiply(multiply(X,Y),Z),commutator(Z,multiply(Y,X))),
inference('REWRITE',[status(thm)],[690,3546,theory(equality)]) ).
cnf(3550,plain,
commutator(multiply(X,commutator(Y,Z)),multiply(Z,Y)) = commutator(X,multiply(Z,Y)),
inference('REWRITE',[status(thm)],[2956,3459,theory(equality)]) ).
cnf(3552,plain,
multiply(c,multiply(a,b)) != multiply(multiply(commutator(a,b),c),multiply(b,a)),
inference('REWRITE',[status(thm)],[3486,3547,3550,theory(equality)]) ).
cnf(3557,plain,
X = multiply(commutator(Y,commutator(Y,Z)),X),
inference('PARAMODULATE',[status(thm)],[318,3009,theory(equality)]) ).
cnf(3597,plain,
commutator(multiply(X,Y),commutator(Y,Z)) = commutator(X,commutator(Y,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[commutator_distributes_over_product,3009,theory(equality)]),361,theory(equality)]) ).
cnf(3625,plain,
multiply(multiply(X,Y),Z) = multiply(multiply(commutator(X,Y),Y),multiply(X,Z)),
inference('PARAMODULATE',[status(thm)],[11,3474,theory(equality)]) ).
cnf(3626,plain,
( multiply(X,Y) != multiply(Z,X)
| multiply(commutator(X,Y),Y) = Z ),
inference('PARAMODULATE',[status(thm)],[10,3474,theory(equality)]) ).
cnf(4080,plain,
commutator(multiply(commutator(X,Y),Z),multiply(X,Y)) = commutator(Z,multiply(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[commutator_distributes_over_product,3490,theory(equality)]),3557,theory(equality)]) ).
cnf(4408,plain,
multiply(multiply(commutator(X,Y),Y),commutator(Y,multiply(X,Y))) = Y,
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[245,3625]),4080,theory(equality)]) ).
cnf(4521,plain,
commutator(X,commutator(X,Y)) = commutator(commutator(Y,X),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[848,4408,theory(equality)]),364,3492,3597,theory(equality)]) ).
cnf(4537,plain,
multiply(X,commutator(commutator(X,multiply(Y,X)),X)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[422,4408,theory(equality)]),318,1700,theory(equality)]) ).
cnf(4616,plain,
commutator(multiply(commutator(X,Y),Z),Y) = commutator(Z,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[commutator_distributes_over_product,4521,theory(equality)]),3557,theory(equality)]) ).
cnf(4733,plain,
multiply(multiply(X,Y),commutator(commutator(X,multiply(Z,X)),X)) = multiply(X,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3625,4537,theory(equality)]),3474,associativity_of_multiply,theory(equality)]) ).
cnf(4812,plain,
multiply(commutator(X,Y),multiply(Z,Y)) = multiply(multiply(Y,commutator(Z,Y)),multiply(commutator(X,Y),Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3474,4616,theory(equality)]),2402,associativity_of_multiply,theory(equality)]) ).
cnf(4895,plain,
multiply(commutator(X,multiply(Y,X)),multiply(Y,X)) = multiply(X,Y),
inference('HYPERRESOLVE',[status(thm)],[3626,associativity_of_multiply]) ).
cnf(4979,plain,
commutator(X,Y) = commutator(X,multiply(Y,X)),
inference('HYPERRESOLVE',[status(thm)],[3488,4895]) ).
cnf(5059,plain,
multiply(multiply(X,Y),commutator(commutator(X,Z),X)) = multiply(X,Y),
inference('REWRITE',[status(thm)],[4733,4979,theory(equality)]) ).
cnf(5060,plain,
multiply(X,Y) = multiply(Y,multiply(commutator(X,Y),X)),
inference('REWRITE',[status(thm)],[706,5059,theory(equality)]) ).
cnf(5198,plain,
multiply(multiply(commutator(X,Y),Z),multiply(Y,X)) = multiply(multiply(Z,X),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[13,5060,theory(equality)]),11,4812,89,theory(equality)]) ).
cnf(5216,plain,
$false,
inference('REWRITE',[status(thm)],[3552,associativity_of_multiply,5198,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP401-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.14 % Command : run-snark %s %d
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 13:02:04 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.47 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48 *
% 0.20/0.48 *
% 0.20/0.48 #<PACKAGE "SNARK-USER">
% 0.20/0.48 *
% 0.20/0.48 SNARK-TPTP-OPTIONS
% 0.20/0.48 *
% 0.20/0.48 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.48 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.48 (USE-FACTORING :POS)
% 0.20/0.48 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.48 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.48 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.48 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.48 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.48 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.48 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.48 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.48 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.48 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.48 *
% 0.20/0.48 "."
% 0.20/0.48 *
% 0.20/0.48 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T13:02:04
% 0.20/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n011.cluster.edu at 2022-06-14T13:02:04
% 0.20/0.50
% 6.22/6.41 ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 6.22/6.41
% 6.22/6.41 #||
% 6.22/6.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.22/6.41 % SZS output start Refutation
% See solution above
% 6.22/6.43 ||#
% 6.22/6.43
% 6.22/6.43 ; Summary of computation:
% 6.22/6.43 ; 11827 formulas have been input or derived (from 109 formulas).
% 6.22/6.43 ; 5216 (44%) were retained. Of these,
% 6.22/6.43 ; 1263 (24%) were simplified or subsumed later,
% 6.22/6.43 ; 3953 (76%) are still being kept.
% 6.22/6.43 ;
% 6.22/6.43 ; Run time in seconds excluding printing time:
% 6.22/6.43 ; 0.002 0% Read assertion file (1 call)
% 6.22/6.43 ; 0.001 0% Assert (6 calls)
% 6.22/6.43 ; 0.537 9% Process new row (11,318 calls)
% 6.22/6.43 ; 0.270 5% Resolution (216 calls)
% 6.22/6.43 ; 0.178 3% Paramodulation (108 calls)
% 6.22/6.43 ; 0.051 1% Condensing (3,308 calls)
% 6.22/6.43 ; 0.446 8% Forward subsumption (3,308 calls)
% 6.22/6.43 ; 0.305 5% Backward subsumption (2,169 calls)
% 6.22/6.43 ; 0.561 9% Clause clause subsumption (204,818 calls)
% 6.22/6.43 ; 1.119 19% Forward simplification (11,007 calls)
% 6.22/6.43 ; 0.417 7% Backward simplification (5,215 calls)
% 6.22/6.43 ; 1.953 33% Ordering (204,846 calls)
% 6.22/6.43 ; 0.000 0% Sortal reasoning (32 calls)
% 6.22/6.43 ; 0.000 0% Purity testing (1 call)
% 6.22/6.43 ; 0.084 1% Other
% 6.22/6.43 ; 5.924 Total
% 6.22/6.43 ; 5.949 Real time
% 6.22/6.43 ;
% 6.22/6.43 ; Term-hash-array has 12,021 terms in all.
% 6.22/6.43 ; Feature-vector-row-index has 1,746 entries (1,746 at peak, 2,169 added, 423 deleted).
% 6.22/6.43 ; Feature-vector-row-index has 2,070 nodes (2,279 at peak, 3,325 added, 1,255 deleted).
% 6.22/6.43 ; Retrieved 146,514 possibly forward subsuming rows in 3,308 calls.
% 6.22/6.43 ; Retrieved 76,249 possibly backward subsumed rows in 2,169 calls.
% 6.22/6.43 ; Path-index has 9,179 entries (9,427 at peak, 12,605 added, 3,426 deleted).
% 6.22/6.43 ; Path-index has 4,132 nodes (4,339 at peak, 5,020 added, 888 deleted).
% 6.22/6.43 ; Trie-index has 9,179 entries (9,427 at peak, 12,605 added, 3,426 deleted).
% 6.22/6.43 ; Trie-index has 39,060 nodes (41,844 at peak, 55,976 added, 16,916 deleted).
% 6.22/6.43 ; Retrieved 196,994 generalization terms in 102,834 calls.
% 6.22/6.43 ; Retrieved 69,094 instance terms in 5,271 calls.
% 6.22/6.43 ; Retrieved 546,246 unifiable terms in 1,358 calls.
% 6.22/6.43 ;
% 6.22/6.43 ; The agenda of backward simplifiable rows to process has 18 entries:
% 6.22/6.43 ; 18 with value 0
% 6.22/6.43 ; The agenda of rows to process has 145 entries:
% 6.22/6.43 ; 11 with value 26 19 with value 31 5 with value 35
% 6.22/6.43 ; 29 with value 27 13 with value 32 2 with value 36
% 6.22/6.43 ; 13 with value 28 17 with value 33 2 with value 37
% 6.22/6.43 ; 10 with value 29 11 with value 34 1 with value 39
% 6.22/6.43 ; 12 with value 30
% 6.22/6.43 ; The agenda of rows to give has 3866 entries:
% 6.22/6.43 ; 1 with value (4 18) 155 with value (4 29) 82 with value (4 40)
% 6.22/6.43 ; 2 with value (4 19) 309 with value (4 30) 117 with value (4 41)
% 6.22/6.43 ; 1 with value (4 20) 456 with value (4 31) 26 with value (4 42)
% 6.22/6.43 ; 3 with value (4 21) 459 with value (4 32) 49 with value (4 43)
% 6.22/6.43 ; 12 with value (4 22) 349 with value (4 33) 11 with value (4 44)
% 6.22/6.43 ; 34 with value (4 23) 241 with value (4 34) 20 with value (4 45)
% 6.22/6.43 ; 44 with value (4 24) 210 with value (4 35) 1 with value (4 46)
% 6.22/6.43 ; 88 with value (4 25) 147 with value (4 36) 1 with value (4 47)
% 6.22/6.43 ; 139 with value (4 26) 232 with value (4 37) 1 with value (4 48)
% 6.22/6.43 ; 172 with value (4 27) 164 with value (4 38) 1 with value (4 49)
% 6.22/6.43 ; 131 with value (4 28) 207 with value (4 39) 1 with value (4 56)
% 6.22/6.43 Evaluation took:
% 6.22/6.43 5.95 seconds of real time
% 6.22/6.43 5.365123 seconds of user run time
% 6.22/6.43 0.585031 seconds of system run time
% 6.22/6.43 [Run times include 0.493 seconds GC run time.]
% 6.22/6.43 0 calls to %EVAL
% 6.22/6.43 0 page faults and
% 6.22/6.43 414,217,696 bytes consed.
% 6.22/6.43 :PROOF-FOUND
% 6.22/6.43 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T13:02:10
% 6.22/6.43 :PROOF-FOUND
% 6.22/6.43 *
%------------------------------------------------------------------------------