TSTP Solution File: GRP002-3 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP002-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n006.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 11:35:09 EDT 2022
% Result : Unsatisfiable 1.09s 1.26s
% Output : Refutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 6
% Syntax : Number of clauses : 114 ( 114 unt; 0 nHn; 3 RR)
% Number of literals : 114 ( 113 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 229 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(associativity,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(commutator,axiom,
commutator(X,Y) = multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator) ).
cnf(5,plain,
commutator(X,Y) = multiply(X,multiply(multiply(Y,inverse(X)),inverse(Y))),
inference('REWRITE',[status(thm)],[commutator,associativity,theory(equality)]) ).
cnf(x_cubed_is_identity,hypothesis,
multiply(X,multiply(X,X)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity) ).
cnf(prove_commutator,negated_conjecture,
commutator(commutator(a,b),b) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutator) ).
cnf(8,plain,
multiply(multiply(X,X),X) = identity,
inference('PARAMODULATE',[status(thm)],[x_cubed_is_identity,associativity,theory(equality)]) ).
cnf(9,plain,
multiply(multiply(X,identity),Y) = multiply(X,Y),
inference('PARAMODULATE',[status(thm)],[associativity,left_identity,theory(equality)]) ).
cnf(10,plain,
X = multiply(inverse(Y),multiply(Y,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).
cnf(11,plain,
multiply(multiply(X,inverse(Y)),Y) = multiply(X,identity),
inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]) ).
cnf(12,plain,
multiply(multiply(X,Y),multiply(Y,Y)) = multiply(X,identity),
inference('PARAMODULATE',[status(thm)],[associativity,x_cubed_is_identity,theory(equality)]) ).
cnf(14,plain,
multiply(multiply(X,multiply(Y,Z)),U) = multiply(multiply(X,Y),multiply(Z,U)),
inference('PARAMODULATE',[status(thm)],[associativity,associativity,theory(equality)]) ).
cnf(15,plain,
multiply(multiply(X,multiply(Y,Z)),U) = multiply(X,multiply(Y,multiply(Z,U))),
inference('PARAMODULATE',[status(thm)],[associativity,associativity,theory(equality)]) ).
cnf(17,plain,
multiply(multiply(multiply(X,Y),Z),U) = multiply(X,multiply(multiply(Y,Z),U)),
inference('PARAMODULATE',[status(thm)],[associativity,associativity,theory(equality)]) ).
cnf(18,plain,
commutator(X,Y) = multiply(multiply(X,Y),multiply(inverse(X),inverse(Y))),
inference('REWRITE',[status(thm)],[5,associativity,17,theory(equality)]) ).
cnf(19,plain,
multiply(multiply(X,Y),multiply(Z,U)) = multiply(X,multiply(multiply(Y,Z),U)),
inference('PARAMODULATE',[status(thm)],[associativity,associativity,theory(equality)]) ).
cnf(21,plain,
commutator(identity,X) = multiply(multiply(X,inverse(identity)),inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,left_identity,theory(equality)]),associativity,theory(equality)]) ).
cnf(28,plain,
commutator(multiply(X,Y),multiply(inverse(X),inverse(Y))) = multiply(multiply(commutator(X,Y),inverse(multiply(X,Y))),inverse(multiply(inverse(X),inverse(Y)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,18,theory(equality)]),associativity,theory(equality)]) ).
cnf(29,plain,
multiply(multiply(multiply(X,Y),X),multiply(multiply(Y,X),Y)) = identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity,8,theory(equality)]),14,15,theory(equality)]) ).
cnf(32,plain,
X = multiply(inverse(identity),X),
inference('PARAMODULATE',[status(thm)],[10,left_identity,theory(equality)]) ).
cnf(33,plain,
X = multiply(inverse(inverse(X)),identity),
inference('PARAMODULATE',[status(thm)],[10,left_inverse,theory(equality)]) ).
cnf(34,plain,
multiply(X,X) = multiply(inverse(X),identity),
inference('PARAMODULATE',[status(thm)],[10,x_cubed_is_identity,theory(equality)]) ).
cnf(35,plain,
X = multiply(inverse(X),inverse(X)),
inference('REWRITE',[status(thm)],[33,34,theory(equality)]) ).
cnf(36,plain,
multiply(X,Y) = multiply(inverse(inverse(X)),Y),
inference('PARAMODULATE',[status(thm)],[10,10,theory(equality)]) ).
cnf(40,plain,
commutator(inverse(X),multiply(X,Y)) = multiply(multiply(Y,X),inverse(multiply(X,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,10,theory(equality)]),associativity,36,theory(equality)]) ).
cnf(41,plain,
inverse(identity) = identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,32,theory(equality)]),32,theory(equality)]) ).
cnf(42,plain,
commutator(identity,X) = multiply(X,inverse(X)),
inference('REWRITE',[status(thm)],[21,9,41,theory(equality)]) ).
cnf(45,plain,
commutator(identity,X) = identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8,35,theory(equality)]),42,theory(equality)]) ).
cnf(46,plain,
identity = multiply(X,inverse(X)),
inference('REWRITE',[status(thm)],[42,45,theory(equality)]) ).
cnf(48,plain,
inverse(X) = multiply(X,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10,35,theory(equality)]),36,theory(equality)]) ).
cnf(49,plain,
X = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[35,48,theory(equality)]) ).
cnf(50,plain,
multiply(multiply(X,Y),inverse(Y)) = multiply(X,identity),
inference('REWRITE',[status(thm)],[12,48,theory(equality)]) ).
cnf(52,plain,
inverse(X) = multiply(inverse(X),identity),
inference('REWRITE',[status(thm)],[34,48,theory(equality)]) ).
cnf(53,plain,
X = multiply(Y,multiply(inverse(Y),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity,46,theory(equality)]),left_identity,theory(equality)]) ).
cnf(54,plain,
commutator(inverse(X),Y) = multiply(multiply(inverse(X),Y),multiply(X,inverse(Y))),
inference('PARAMODULATE',[status(thm)],[18,49,theory(equality)]) ).
cnf(56,plain,
multiply(inverse(X),Y) = multiply(X,multiply(X,Y)),
inference('PARAMODULATE',[status(thm)],[associativity,48,theory(equality)]) ).
cnf(57,plain,
multiply(multiply(X,Y),Y) = multiply(X,inverse(Y)),
inference('PARAMODULATE',[status(thm)],[associativity,48,theory(equality)]) ).
cnf(58,plain,
X = multiply(X,identity),
inference('PARAMODULATE',[status(thm)],[52,49,theory(equality)]) ).
cnf(59,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference('REWRITE',[status(thm)],[11,58,theory(equality)]) ).
cnf(60,plain,
multiply(multiply(X,Y),inverse(Y)) = X,
inference('REWRITE',[status(thm)],[50,58,theory(equality)]) ).
cnf(61,plain,
inverse(X) = multiply(inverse(multiply(Y,X)),Y),
inference('PARAMODULATE',[status(thm)],[10,60,theory(equality)]) ).
cnf(62,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference('PARAMODULATE',[status(thm)],[60,10,theory(equality)]) ).
cnf(65,plain,
multiply(commutator(X,Y),inverse(multiply(inverse(X),inverse(Y)))) = multiply(X,Y),
inference('PARAMODULATE',[status(thm)],[60,18,theory(equality)]) ).
cnf(66,plain,
commutator(multiply(X,Y),inverse(Y)) = multiply(X,multiply(inverse(multiply(X,Y)),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[18,60,theory(equality)]),49,theory(equality)]) ).
cnf(67,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference('PARAMODULATE',[status(thm)],[60,61,theory(equality)]) ).
cnf(71,plain,
commutator(X,Y) = commutator(inverse(Y),multiply(Y,X)),
inference('REWRITE',[status(thm)],[18,40,67,theory(equality)]) ).
cnf(72,plain,
commutator(X,Y) = multiply(multiply(X,Y),inverse(multiply(Y,X))),
inference('REWRITE',[status(thm)],[40,71,theory(equality)]) ).
cnf(73,plain,
commutator(multiply(X,Y),inverse(multiply(Y,X))) = multiply(multiply(commutator(X,Y),inverse(multiply(X,Y))),multiply(Y,X)),
inference('REWRITE',[status(thm)],[28,49,67,theory(equality)]) ).
cnf(75,plain,
multiply(commutator(X,Y),multiply(Y,X)) = multiply(X,Y),
inference('REWRITE',[status(thm)],[65,49,67,theory(equality)]) ).
cnf(76,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[59,61,theory(equality)]) ).
cnf(78,plain,
commutator(multiply(X,Y),inverse(Y)) = multiply(X,inverse(multiply(inverse(Y),multiply(X,Y)))),
inference('REWRITE',[status(thm)],[66,76,theory(equality)]) ).
cnf(80,plain,
commutator(multiply(X,Y),inverse(X)) = commutator(X,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[71,10,theory(equality)]),49,theory(equality)]) ).
cnf(81,plain,
commutator(multiply(inverse(X),Y),X) = commutator(inverse(X),Y),
inference('PARAMODULATE',[status(thm)],[71,53,theory(equality)]) ).
cnf(83,plain,
commutator(multiply(X,Y),Z) = commutator(inverse(Z),multiply(multiply(Z,X),Y)),
inference('PARAMODULATE',[status(thm)],[71,associativity,theory(equality)]) ).
cnf(85,plain,
inverse(multiply(X,inverse(Y))) = multiply(Y,inverse(X)),
inference('PARAMODULATE',[status(thm)],[53,62,theory(equality)]) ).
cnf(86,plain,
commutator(multiply(X,Y),inverse(Y)) = inverse(commutator(inverse(Y),X)),
inference('REWRITE',[status(thm)],[78,54,14,85,theory(equality)]) ).
cnf(87,plain,
commutator(multiply(X,Y),inverse(multiply(Y,X))) = inverse(multiply(inverse(multiply(Y,X)),multiply(multiply(X,Y),inverse(commutator(X,Y))))),
inference('REWRITE',[status(thm)],[73,76,85,theory(equality)]) ).
cnf(88,plain,
commutator(X,inverse(multiply(X,Y))) = inverse(commutator(inverse(Y),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[80,60,theory(equality)]),86,theory(equality)]) ).
cnf(89,plain,
commutator(multiply(multiply(X,Y),Z),inverse(X)) = commutator(X,multiply(Y,Z)),
inference('PARAMODULATE',[status(thm)],[80,associativity,theory(equality)]) ).
cnf(95,plain,
commutator(inverse(X),inverse(Y)) = commutator(Y,inverse(multiply(X,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[71,67,theory(equality)]),49,theory(equality)]) ).
cnf(100,plain,
multiply(commutator(X,Y),Y) = multiply(multiply(X,Y),inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[75,10,theory(equality)]),80,theory(equality)]) ).
cnf(101,plain,
commutator(multiply(X,Y),inverse(commutator(X,Y))) = commutator(commutator(X,Y),multiply(Y,X)),
inference('PARAMODULATE',[status(thm)],[80,75,theory(equality)]) ).
cnf(104,plain,
multiply(commutator(inverse(X),Y),Y) = multiply(inverse(X),multiply(Y,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[75,53,theory(equality)]),associativity,81,theory(equality)]) ).
cnf(113,plain,
commutator(multiply(X,Y),X) = commutator(inverse(X),multiply(inverse(X),Y)),
inference('PARAMODULATE',[status(thm)],[71,56,theory(equality)]) ).
cnf(147,plain,
multiply(multiply(X,Y),inverse(Z)) = multiply(X,inverse(multiply(Z,inverse(Y)))),
inference('PARAMODULATE',[status(thm)],[associativity,85,theory(equality)]) ).
cnf(148,plain,
inverse(multiply(X,multiply(Y,inverse(Z)))) = multiply(Z,inverse(multiply(X,Y))),
inference('PARAMODULATE',[status(thm)],[85,associativity,theory(equality)]) ).
cnf(189,plain,
commutator(X,Y) = inverse(commutator(Y,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity,72,theory(equality)]),58,46,148,100,85,theory(equality)]) ).
cnf(193,plain,
commutator(multiply(X,Y),inverse(multiply(Y,X))) = inverse(multiply(inverse(multiply(Y,X)),multiply(multiply(X,Y),commutator(Y,X)))),
inference('REWRITE',[status(thm)],[87,189,theory(equality)]) ).
cnf(195,plain,
commutator(multiply(X,Y),commutator(Y,X)) = commutator(commutator(X,Y),multiply(Y,X)),
inference('REWRITE',[status(thm)],[101,189,theory(equality)]) ).
cnf(198,plain,
commutator(multiply(X,Y),inverse(Y)) = commutator(X,inverse(Y)),
inference('REWRITE',[status(thm)],[86,189,theory(equality)]) ).
cnf(199,plain,
commutator(X,inverse(multiply(X,Y))) = commutator(X,inverse(Y)),
inference('REWRITE',[status(thm)],[88,189,theory(equality)]) ).
cnf(200,plain,
commutator(inverse(X),multiply(Y,X)) = commutator(inverse(X),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[72,60,theory(equality)]),58,41,46,147,104,theory(equality)]) ).
cnf(202,plain,
commutator(commutator(X,Y),inverse(multiply(X,Y))) = commutator(multiply(X,Y),inverse(multiply(Y,X))),
inference('PARAMODULATE',[status(thm)],[80,72,theory(equality)]) ).
cnf(203,plain,
commutator(commutator(X,Y),inverse(multiply(X,Y))) = inverse(multiply(inverse(multiply(Y,X)),multiply(multiply(X,Y),commutator(Y,X)))),
inference('REWRITE',[status(thm)],[193,202,theory(equality)]) ).
cnf(204,plain,
commutator(inverse(multiply(X,Y)),multiply(Y,X)) = commutator(inverse(multiply(Y,X)),commutator(Y,X)),
inference('PARAMODULATE',[status(thm)],[71,72,theory(equality)]) ).
cnf(205,plain,
commutator(inverse(X),inverse(Y)) = multiply(inverse(multiply(Y,X)),multiply(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[72,67,theory(equality)]),49,67,theory(equality)]) ).
cnf(214,plain,
commutator(inverse(multiply(X,Y)),commutator(X,Y)) = multiply(commutator(inverse(X),inverse(Y)),commutator(Y,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[72,72,theory(equality)]),189,205,204,theory(equality)]) ).
cnf(219,plain,
identity = multiply(commutator(X,Y),commutator(Y,X)),
inference('PARAMODULATE',[status(thm)],[46,189,theory(equality)]) ).
cnf(229,plain,
commutator(X,Y) = commutator(multiply(X,Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[198,60,theory(equality)]),49,theory(equality)]) ).
cnf(232,plain,
commutator(inverse(X),inverse(Y)) = commutator(inverse(X),inverse(multiply(X,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[198,10,theory(equality)]),95,theory(equality)]) ).
cnf(236,plain,
commutator(commutator(X,Y),inverse(multiply(X,Y))) = commutator(commutator(X,Y),inverse(multiply(Y,X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[198,75,theory(equality)]),202,theory(equality)]) ).
cnf(239,plain,
commutator(commutator(X,Y),multiply(Y,X)) = commutator(multiply(X,Y),multiply(Y,X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[198,72,theory(equality)]),49,theory(equality)]) ).
cnf(302,plain,
commutator(X,inverse(multiply(multiply(X,Y),Z))) = commutator(X,inverse(multiply(Y,Z))),
inference('PARAMODULATE',[status(thm)],[199,associativity,theory(equality)]) ).
cnf(308,plain,
inverse(multiply(multiply(X,Y),X)) = multiply(multiply(Y,X),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[60,29,theory(equality)]),left_identity,theory(equality)]) ).
cnf(361,plain,
commutator(multiply(multiply(X,Y),Z),X) = commutator(inverse(X),multiply(multiply(inverse(X),Y),Z)),
inference('PARAMODULATE',[status(thm)],[83,56,theory(equality)]) ).
cnf(400,plain,
commutator(X,multiply(X,Y)) = multiply(multiply(inverse(X),Y),multiply(multiply(Y,X),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[72,308,theory(equality)]),56,theory(equality)]) ).
cnf(862,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(Z,U)) = multiply(inverse(Y),multiply(multiply(X,Z),U)),
inference('PARAMODULATE',[status(thm)],[19,76,theory(equality)]) ).
cnf(863,plain,
commutator(commutator(X,Y),inverse(multiply(X,Y))) = multiply(inverse(multiply(Y,commutator(Y,X))),multiply(commutator(inverse(X),Y),Y)),
inference('REWRITE',[status(thm)],[203,49,76,104,862,theory(equality)]) ).
cnf(864,plain,
multiply(multiply(X,inverse(Y)),multiply(Z,U)) = multiply(multiply(X,Y),multiply(multiply(Y,Z),U)),
inference('PARAMODULATE',[status(thm)],[19,57,theory(equality)]) ).
cnf(865,plain,
commutator(X,multiply(X,Y)) = commutator(inverse(X),inverse(Y)),
inference('REWRITE',[status(thm)],[400,205,67,864,theory(equality)]) ).
cnf(866,plain,
commutator(multiply(X,Y),X) = commutator(X,inverse(Y)),
inference('REWRITE',[status(thm)],[113,49,865,theory(equality)]) ).
cnf(1003,plain,
commutator(X,inverse(Y)) = commutator(inverse(Y),inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[189,865,theory(equality)]),189,866,theory(equality)]) ).
cnf(1009,plain,
commutator(X,inverse(Y)) = multiply(inverse(multiply(X,Y)),multiply(Y,X)),
inference('REWRITE',[status(thm)],[205,1003,theory(equality)]) ).
cnf(1011,plain,
commutator(inverse(multiply(X,Y)),commutator(X,Y)) = multiply(commutator(Y,inverse(X)),commutator(Y,X)),
inference('REWRITE',[status(thm)],[214,1003,theory(equality)]) ).
cnf(1012,plain,
commutator(X,inverse(Y)) = commutator(Y,X),
inference('REWRITE',[status(thm)],[232,80,1003,theory(equality)]) ).
cnf(1026,plain,
commutator(multiply(multiply(X,Y),Z),X) = commutator(multiply(Y,Z),X),
inference('REWRITE',[status(thm)],[302,1012,theory(equality)]) ).
cnf(1028,plain,
commutator(multiply(X,Y),Z) = commutator(inverse(Z),multiply(multiply(inverse(Z),X),Y)),
inference('REWRITE',[status(thm)],[361,1026,theory(equality)]) ).
cnf(1030,plain,
commutator(multiply(X,Y),commutator(X,Y)) = commutator(multiply(Y,X),commutator(X,Y)),
inference('REWRITE',[status(thm)],[236,1012,theory(equality)]) ).
cnf(1031,plain,
commutator(multiply(X,Y),commutator(X,Y)) = multiply(inverse(multiply(Y,commutator(Y,X))),multiply(commutator(inverse(X),Y),Y)),
inference('REWRITE',[status(thm)],[863,1012,theory(equality)]) ).
cnf(1053,plain,
commutator(inverse(multiply(X,Y)),commutator(X,Y)) = identity,
inference('REWRITE',[status(thm)],[1011,219,1012,theory(equality)]) ).
cnf(1054,plain,
commutator(inverse(multiply(X,Y)),multiply(Y,X)) = identity,
inference('REWRITE',[status(thm)],[204,1053,theory(equality)]) ).
cnf(1057,plain,
commutator(X,multiply(multiply(X,Y),Z)) = commutator(X,multiply(Y,Z)),
inference('REWRITE',[status(thm)],[89,1012,theory(equality)]) ).
cnf(1059,plain,
commutator(multiply(X,Y),Z) = commutator(inverse(Z),multiply(X,Y)),
inference('REWRITE',[status(thm)],[1028,1057,theory(equality)]) ).
cnf(1069,plain,
commutator(commutator(X,Y),multiply(Y,X)) = identity,
inference('REWRITE',[status(thm)],[1054,239,1059,theory(equality)]) ).
cnf(1070,plain,
commutator(multiply(X,Y),commutator(Y,X)) = identity,
inference('REWRITE',[status(thm)],[195,1069,theory(equality)]) ).
cnf(1071,plain,
commutator(multiply(X,Y),commutator(X,Y)) = identity,
inference('REWRITE',[status(thm)],[1030,1070,theory(equality)]) ).
cnf(1072,plain,
identity = multiply(inverse(multiply(X,commutator(X,Y))),multiply(commutator(inverse(Y),X),X)),
inference('REWRITE',[status(thm)],[1031,1071,theory(equality)]) ).
cnf(1098,plain,
commutator(X,Y) = commutator(inverse(Y),X),
inference('REWRITE',[status(thm)],[200,229,1059,theory(equality)]) ).
cnf(1100,plain,
identity = multiply(inverse(multiply(X,commutator(X,Y))),multiply(commutator(X,Y),X)),
inference('REWRITE',[status(thm)],[1072,1098,theory(equality)]) ).
cnf(1119,plain,
commutator(X,Y) = multiply(inverse(multiply(Y,X)),multiply(X,Y)),
inference('REWRITE',[status(thm)],[1009,1012,theory(equality)]) ).
cnf(1120,plain,
identity = commutator(commutator(X,Y),X),
inference('REWRITE',[status(thm)],[1100,1119,theory(equality)]) ).
cnf(1131,plain,
identity = commutator(commutator(X,Y),Y),
inference('PARAMODULATE',[status(thm)],[1120,1012,theory(equality)]) ).
cnf(1132,plain,
$false,
inference('REWRITE',[status(thm)],[prove_commutator,1131,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP002-3 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : run-snark %s %d
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 00:53:11 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.46 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47 *
% 0.20/0.47 *
% 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 2022-06-14T00:53:12
% 0.20/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n006.cluster.edu at 2022-06-14T00:53:12
% 0.20/0.49
% 0.20/0.49 ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.20/0.49 ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 1.09/1.26 ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 1.09/1.26
% 1.09/1.26 #||
% 1.09/1.26 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.09/1.26 % SZS output start Refutation
% See solution above
% 1.09/1.28 ||#
% 1.09/1.28
% 1.09/1.28 ; Summary of computation:
% 1.09/1.28 ; 3230 formulas have been input or derived (from 69 formulas).
% 1.09/1.28 ; 1132 (35%) were retained. Of these,
% 1.09/1.28 ; 365 (32%) were simplified or subsumed later,
% 1.09/1.28 ; 767 (68%) are still being kept.
% 1.09/1.28 ;
% 1.09/1.28 ; Run time in seconds excluding printing time:
% 1.09/1.28 ; 0.002 0% Read assertion file (1 call)
% 1.09/1.28 ; 0.001 0% Assert (6 calls)
% 1.09/1.28 ; 0.098 13% Process new row (3,194 calls)
% 1.09/1.28 ; 0.006 1% Resolution (136 calls)
% 1.09/1.28 ; 0.036 5% Paramodulation (68 calls)
% 1.09/1.28 ; 0.196 25% Forward simplification (3,097 calls)
% 1.09/1.28 ; 0.065 8% Backward simplification (1,131 calls)
% 1.09/1.28 ; 0.343 44% Ordering (44,627 calls)
% 1.09/1.28 ; 0.000 0% Sortal reasoning (32 calls)
% 1.09/1.28 ; 0.000 0% Purity testing (1 call)
% 1.09/1.28 ; 0.035 4% Other
% 1.09/1.28 ; 0.782 Total
% 1.09/1.28 ; 0.798 Real time
% 1.09/1.28 ;
% 1.09/1.28 ; Term-hash-array has 2,659 terms in all.
% 1.09/1.28 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 1.09/1.28 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 1.09/1.28 ; Path-index has 1,879 entries (2,111 at peak, 2,808 added, 929 deleted).
% 1.09/1.28 ; Path-index has 2,007 nodes (2,131 at peak, 2,424 added, 417 deleted).
% 1.09/1.28 ; Trie-index has 1,879 entries (2,111 at peak, 2,808 added, 929 deleted).
% 1.09/1.28 ; Trie-index has 8,944 nodes (10,510 at peak, 13,374 added, 4,430 deleted).
% 1.09/1.28 ; Retrieved 73,498 generalization terms in 27,463 calls.
% 1.09/1.28 ; Retrieved 11,418 instance terms in 2,027 calls.
% 1.09/1.28 ; Retrieved 8,348 unifiable terms in 421 calls.
% 1.09/1.28 ;
% 1.09/1.28 ; The agenda of rows to process has 19 entries:
% 1.09/1.28 ; 1 with value 15 6 with value 19 2 with value 22
% 1.09/1.28 ; 2 with value 16 6 with value 21 1 with value 23
% 1.09/1.28 ; 1 with value 18
% 1.09/1.28 ; The agenda of rows to give has 723 entries:
% 1.09/1.28 ; 4 with value (4 14) 10 with value (4 22) 42 with value (4 29)
% 1.09/1.28 ; 5 with value (4 15) 37 with value (4 23) 96 with value (4 30)
% 1.09/1.28 ; 3 with value (4 17) 39 with value (4 24) 143 with value (4 31)
% 1.09/1.28 ; 3 with value (4 18) 28 with value (4 25) 18 with value (4 32)
% 1.09/1.28 ; 6 with value (4 19) 90 with value (4 26) 34 with value (4 33)
% 1.09/1.28 ; 8 with value (4 20) 47 with value (4 27) 3 with value (4 34)
% 1.09/1.28 ; 23 with value (4 21) 82 with value (4 28) 2 with value (4 35)
% 1.09/1.28 Evaluation took:
% 1.09/1.28 0.798 seconds of real time
% 1.09/1.28 0.731604 seconds of user run time
% 1.09/1.28 0.067138 seconds of system run time
% 1.09/1.28 [Run times include 0.03 seconds GC run time.]
% 1.09/1.28 0 calls to %EVAL
% 1.09/1.28 0 page faults and
% 1.09/1.28 59,726,544 bytes consed.
% 1.09/1.28 :PROOF-FOUND
% 1.09/1.28 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T00:53:12
% 1.09/1.28 :PROOF-FOUND
% 1.09/1.28 *
%------------------------------------------------------------------------------