%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP024-5 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% 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 : 300s
% DateTime : Tue Jul 15 06:43:18 AM UTC 2025
% Result : Unsatisfiable 103.11s 103.37s
% Output : CNFRefutation 103.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 6
% Syntax : Number of clauses : 107 ( 107 unt; 0 nHn; 4 RR)
% Number of literals : 107 ( 106 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 245 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(a,commutator(b,c)) != multiply(commutator(b,c),a),
file('theBenchmark.p',prove_center) ).
cnf(c1,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c2,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c3,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c4,axiom,
commutator(commutator(X,Y),Z) = commutator(X,commutator(Y,Z)),
file('theBenchmark.p',associativity_of_commutator) ).
cnf(c5,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c1,c2,c3]) ).
cnf(c7,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c8,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c5]) ).
cnf(c9,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c7,c8]) ).
cnf(c10,plain,
inverse(identity) = identity,
inference(equational,[status(thm)],[c2,c9]) ).
cnf(c11,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c7,c9]) ).
cnf(c12,plain,
multiply(X,inverse(X)) = identity,
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c13,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c14,axiom,
commutator(X,Y) = multiply(inverse(X),multiply(inverse(Y),multiply(X,Y))),
file('theBenchmark.p',name) ).
cnf(c15,plain,
multiply(inverse(X),multiply(inverse(Y),multiply(X,Y))) = commutator(X,Y),
inference(equational,[status(thm)],[c14]) ).
cnf(c16,plain,
commutator(identity,X) = identity,
inference(equational,[status(thm)],[c1,c2,c10,c15]) ).
cnf(c17,plain,
commutator(X,X) = identity,
inference(equational,[status(thm)],[c2,c5,c15]) ).
cnf(c18,plain,
commutator(inverse(X),X) = identity,
inference(equational,[status(thm)],[c2,c9,c11,c12,c15]) ).
cnf(c19,plain,
commutator(X,identity) = identity,
inference(equational,[status(thm)],[c1,c2,c7,c10,c11,c15]) ).
cnf(c21,plain,
commutator(X,commutator(X,Y)) = identity,
inference(equational,[status(thm)],[c4,c16,c17]) ).
cnf(c22,plain,
commutator(inverse(X),commutator(X,Y)) = identity,
inference(equational,[status(thm)],[c4,c16,c18]) ).
cnf(c23,plain,
multiply(X,commutator(X,Y)) = multiply(inverse(Y),multiply(X,Y)),
inference(equational,[status(thm)],[c5,c11,c15]) ).
cnf(c25,plain,
multiply(X,commutator(X,inverse(Y))) = multiply(Y,multiply(X,inverse(Y))),
inference(equational,[status(thm)],[c8,c23]) ).
cnf(c27,plain,
multiply(X,multiply(Y,commutator(Y,X))) = multiply(Y,X),
inference(equational,[status(thm)],[c5,c11,c23]) ).
cnf(c28,plain,
multiply(commutator(X,Y),X) = multiply(X,commutator(X,Y)),
inference(equational,[status(thm)],[c9,c21,c27]) ).
cnf(c29,plain,
commutator(X,commutator(Y,X)) = identity,
inference(equational,[status(thm)],[c2,c4,c5,c15,c28]) ).
cnf(c30,plain,
multiply(commutator(X,Y),Y) = multiply(Y,commutator(X,Y)),
inference(equational,[status(thm)],[c9,c27,c29]) ).
cnf(c31,plain,
multiply(commutator(X,Y),inverse(X)) = multiply(inverse(X),commutator(X,Y)),
inference(equational,[status(thm)],[c9,c22,c27]) ).
cnf(c32,plain,
commutator(X,commutator(Y,inverse(X))) = identity,
inference(equational,[status(thm)],[c2,c4,c11,c13,c15,c31]) ).
cnf(c33,plain,
commutator(inverse(X),commutator(Y,X)) = identity,
inference(equational,[status(thm)],[c11,c32]) ).
cnf(c35,plain,
multiply(X,multiply(inverse(multiply(X,Y)),Y)) = commutator(inverse(X),multiply(X,Y)),
inference(equational,[status(thm)],[c5,c11,c15]) ).
cnf(c36,plain,
multiply(X,multiply(Y,inverse(multiply(X,Y)))) = identity,
inference(equational,[status(thm)],[c3,c12]) ).
cnf(c37,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(equational,[status(thm)],[c5,c9,c36]) ).
cnf(c38,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c5,c37]) ).
cnf(c39,plain,
inverse(multiply(X,inverse(Y))) = multiply(Y,inverse(X)),
inference(equational,[status(thm)],[c13,c37]) ).
cnf(c40,plain,
multiply(inverse(multiply(X,Y)),X) = inverse(Y),
inference(equational,[status(thm)],[c11,c37]) ).
cnf(c41,plain,
inverse(multiply(inverse(X),Y)) = multiply(inverse(Y),X),
inference(equational,[status(thm)],[c13,c40]) ).
cnf(c48,plain,
multiply(inverse(multiply(X,Y)),multiply(X,multiply(Y,Z))) = Z,
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c51,plain,
multiply(inverse(multiply(X,Y)),multiply(Y,X)) = commutator(Y,X),
inference(equational,[status(thm)],[c27,c48]) ).
cnf(c52,plain,
inverse(commutator(X,Y)) = commutator(Y,X),
inference(equational,[status(thm)],[c41,c51]) ).
cnf(c53,plain,
commutator(multiply(inverse(X),Y),X) = commutator(Y,X),
inference(equational,[status(thm)],[c3,c13,c15,c51]) ).
cnf(c55,plain,
commutator(X,multiply(inverse(X),Y)) = commutator(X,Y),
inference(equational,[status(thm)],[c3,c13,c41,c51]) ).
cnf(c56,plain,
commutator(X,multiply(X,Y)) = commutator(X,Y),
inference(equational,[status(thm)],[c5,c55]) ).
cnf(c57,plain,
commutator(inverse(X),multiply(Y,X)) = commutator(Y,X),
inference(equational,[status(thm)],[c3,c5,c9,c12,c23,c51]) ).
cnf(c58,plain,
commutator(multiply(X,Y),inverse(Y)) = commutator(Y,X),
inference(equational,[status(thm)],[c3,c9,c12,c23,c40,c51,c52]) ).
cnf(c60,plain,
commutator(multiply(X,inverse(Y)),Y) = commutator(inverse(Y),X),
inference(equational,[status(thm)],[c2,c3,c9,c25,c40,c51,c52]) ).
cnf(c61,plain,
commutator(multiply(X,Y),inverse(X)) = commutator(Y,inverse(X)),
inference(equational,[status(thm)],[c11,c53]) ).
cnf(c62,plain,
commutator(inverse(X),multiply(X,Y)) = commutator(inverse(X),Y),
inference(equational,[status(thm)],[c11,c55]) ).
cnf(c63,plain,
commutator(multiply(X,commutator(X,Y)),Y) = commutator(X,Y),
inference(equational,[status(thm)],[c3,c27,c30,c48,c51]) ).
cnf(c64,plain,
commutator(inverse(X),Y) = commutator(Y,X),
inference(equational,[status(thm)],[c3,c27,c53,c60,c63]) ).
cnf(c65,plain,
commutator(X,inverse(Y)) = commutator(Y,X),
inference(equational,[status(thm)],[c3,c27,c58,c61,c63]) ).
cnf(c66,plain,
commutator(multiply(X,Y),Y) = commutator(X,Y),
inference(equational,[status(thm)],[c23,c53,c63]) ).
cnf(c72,plain,
multiply(commutator(X,Y),inverse(Y)) = multiply(inverse(Y),commutator(X,Y)),
inference(equational,[status(thm)],[c28,c57]) ).
cnf(c74,plain,
multiply(commutator(X,Y),multiply(Y,X)) = multiply(X,Y),
inference(equational,[status(thm)],[c3,c27,c28,c58]) ).
cnf(c75,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(Y),Z),
inference(equational,[status(thm)],[c13,c48]) ).
cnf(c78,plain,
multiply(commutator(X,Y),commutator(Y,X)) = identity,
inference(equational,[status(thm)],[c4,c29,c35,c51,c52,c56,c74]) ).
cnf(c80,plain,
multiply(X,multiply(commutator(X,Y),Z)) = multiply(inverse(Y),multiply(X,multiply(Y,Z))),
inference(equational,[status(thm)],[c3,c23]) ).
cnf(c82,plain,
multiply(inverse(X),multiply(inverse(Y),Z)) = multiply(inverse(multiply(Y,X)),Z),
inference(equational,[status(thm)],[c5,c75]) ).
cnf(c92,plain,
multiply(inverse(X),multiply(Y,multiply(X,inverse(Y)))) = commutator(Y,X),
inference(equational,[status(thm)],[c8,c15,c65]) ).
cnf(c93,plain,
multiply(X,multiply(Y,inverse(multiply(Y,X)))) = commutator(X,Y),
inference(equational,[status(thm)],[c8,c38,c65,c92]) ).
cnf(c102,plain,
multiply(X,inverse(multiply(X,commutator(Y,X)))) = commutator(X,Y),
inference(equational,[status(thm)],[c3,c5,c25,c60,c64,c65,c93]) ).
cnf(c103,plain,
multiply(inverse(X),commutator(X,Y)) = inverse(multiply(X,commutator(Y,X))),
inference(equational,[status(thm)],[c48,c75,c102]) ).
cnf(c104,plain,
multiply(inverse(X),commutator(Y,X)) = inverse(multiply(X,commutator(X,Y))),
inference(equational,[status(thm)],[c64,c65,c103]) ).
cnf(c110,plain,
multiply(X,multiply(commutator(Y,X),Z)) = multiply(Y,multiply(X,multiply(inverse(Y),Z))),
inference(equational,[status(thm)],[c8,c65,c80]) ).
cnf(c111,plain,
multiply(X,inverse(multiply(X,commutator(X,Y)))) = commutator(Y,X),
inference(equational,[status(thm)],[c5,c23,c28,c64,c65,c104,c110]) ).
cnf(c114,plain,
multiply(commutator(X,Y),multiply(Y,Z)) = multiply(Y,multiply(commutator(X,Y),Z)),
inference(equational,[status(thm)],[c3,c11,c52,c75,c102]) ).
cnf(c120,plain,
multiply(inverse(X),commutator(Y,Z)) = inverse(multiply(commutator(Z,Y),X)),
inference(equational,[status(thm)],[c9,c75,c78]) ).
cnf(c121,plain,
commutator(multiply(X,multiply(Y,Z)),Z) = commutator(multiply(X,Y),Z),
inference(equational,[status(thm)],[c3,c66]) ).
cnf(c125,plain,
multiply(X,inverse(multiply(Y,multiply(Z,X)))) = inverse(multiply(Y,Z)),
inference(equational,[status(thm)],[c3,c37]) ).
cnf(c126,plain,
multiply(commutator(X,Y),inverse(Z)) = inverse(multiply(Z,commutator(Y,X))),
inference(equational,[status(thm)],[c3,c5,c28,c39,c72,c120,c125]) ).
cnf(c130,plain,
multiply(commutator(X,Y),commutator(X,commutator(Y,Z))) = multiply(inverse(Z),multiply(commutator(X,Y),Z)),
inference(equational,[status(thm)],[c4,c23]) ).
cnf(c131,plain,
multiply(inverse(X),multiply(Y,multiply(Z,X))) = multiply(Y,multiply(Z,commutator(multiply(Y,Z),X))),
inference(equational,[status(thm)],[c3,c23]) ).
cnf(c140,plain,
multiply(inverse(multiply(X,Y)),multiply(Y,multiply(X,Z))) = multiply(commutator(Y,X),Z),
inference(equational,[status(thm)],[c3,c15,c82]) ).
cnf(c141,plain,
multiply(commutator(X,commutator(Y,Z)),W) = multiply(commutator(Y,commutator(Z,X)),W),
inference(equational,[status(thm)],[c3,c4,c13,c52,c58,c75,c130,c140]) ).
cnf(c166,plain,
multiply(inverse(multiply(X,Y)),multiply(Y,Z)) = multiply(inverse(multiply(X,commutator(X,Y))),Z),
inference(equational,[status(thm)],[c27,c75]) ).
cnf(c176,plain,
commutator(X,multiply(inverse(multiply(Y,X)),Z)) = commutator(X,multiply(inverse(Y),Z)),
inference(equational,[status(thm)],[c55,c82]) ).
cnf(c184,plain,
multiply(X,multiply(Y,commutator(Z,multiply(X,Y)))) = multiply(Z,multiply(X,multiply(Y,inverse(Z)))),
inference(equational,[status(thm)],[c8,c65,c131]) ).
cnf(c193,plain,
commutator(multiply(inverse(multiply(X,Y)),Y),Z) = commutator(Z,multiply(X,commutator(X,Y))),
inference(equational,[status(thm)],[c57,c64,c121,c166]) ).
cnf(c203,plain,
multiply(inverse(X),multiply(Y,multiply(X,multiply(inverse(Y),Z)))) = multiply(commutator(Y,X),Z),
inference(equational,[status(thm)],[c3,c5,c61,c65,c140]) ).
cnf(c204,plain,
multiply(X,multiply(Y,multiply(inverse(multiply(Y,X)),Z))) = multiply(commutator(X,Y),Z),
inference(equational,[status(thm)],[c8,c65,c82,c203]) ).
cnf(c258,plain,
multiply(inverse(X),multiply(Y,multiply(X,commutator(Y,Z)))) = multiply(commutator(Y,X),multiply(inverse(Z),multiply(Y,Z))),
inference(equational,[status(thm)],[c3,c15,c41,c65,c140]) ).
cnf(c259,plain,
multiply(commutator(X,commutator(Y,Z)),commutator(X,Y)) = multiply(inverse(Z),multiply(commutator(X,Y),Z)),
inference(equational,[status(thm)],[c4,c9,c17,c19,c51,c64,c80,c82,c258]) ).
cnf(c269,plain,
multiply(X,multiply(inverse(multiply(X,Y)),multiply(Y,Z))) = multiply(commutator(Y,X),Z),
inference(equational,[status(thm)],[c3,c35,c62,c64]) ).
cnf(c311,plain,
multiply(inverse(multiply(X,Y)),multiply(commutator(X,Y),Z)) = multiply(inverse(multiply(Y,X)),Z),
inference(equational,[status(thm)],[c48,c204]) ).
cnf(c312,plain,
multiply(inverse(multiply(commutator(X,Y),Z)),W) = multiply(inverse(Z),multiply(commutator(Y,X),W)),
inference(equational,[status(thm)],[c3,c41,c75,c204,c311]) ).
cnf(c319,plain,
multiply(commutator(X,Y),commutator(Z,commutator(X,Y))) = multiply(Z,inverse(multiply(Z,commutator(Y,X)))),
inference(equational,[status(thm)],[c3,c51,c126,c140,c184]) ).
cnf(c323,plain,
multiply(inverse(X),multiply(commutator(Y,Z),X)) = multiply(commutator(Y,Z),commutator(X,commutator(Y,Z))),
inference(equational,[status(thm)],[c30,c141,c259]) ).
cnf(c324,plain,
multiply(inverse(X),multiply(commutator(Y,Z),X)) = multiply(X,inverse(multiply(X,commutator(Z,Y)))),
inference(equational,[status(thm)],[c319,c323]) ).
cnf(c374,plain,
multiply(X,commutator(multiply(Y,X),Z)) = multiply(inverse(Z),multiply(commutator(Y,Z),multiply(X,Z))),
inference(equational,[status(thm)],[c5,c64,c80,c131]) ).
cnf(c430,plain,
multiply(inverse(multiply(X,Y)),multiply(Y,commutator(Z,X))) = multiply(commutator(Y,X),multiply(inverse(multiply(X,Z)),Z)),
inference(equational,[status(thm)],[c35,c62,c64,c140]) ).
cnf(c431,plain,
multiply(X,inverse(multiply(X,commutator(Y,Z)))) = multiply(commutator(X,commutator(Y,Z)),commutator(Z,Y)),
inference(equational,[status(thm)],[c3,c9,c11,c22,c111,c126,c312,c324,c430]) ).
cnf(c437,plain,
multiply(X,multiply(X,inverse(multiply(X,commutator(Y,Z))))) = multiply(commutator(Z,Y),X),
inference(equational,[status(thm)],[c9,c52,c78,c80,c431]) ).
cnf(c439,plain,
multiply(X,multiply(commutator(Y,X),commutator(Y,Z))) = multiply(commutator(Y,multiply(Z,X)),X),
inference(equational,[status(thm)],[c28,c41,c269,c312,c374,c437]) ).
cnf(c454,plain,
multiply(commutator(X,Y),multiply(inverse(Z),multiply(Y,Z))) = multiply(X,multiply(Y,inverse(multiply(commutator(Z,Y),X)))),
inference(equational,[status(thm)],[c8,c65,c120,c258]) ).
cnf(c498,plain,
multiply(X,multiply(inverse(multiply(X,Y)),multiply(Z,Y))) = multiply(Z,commutator(multiply(inverse(X),Z),Y)),
inference(equational,[status(thm)],[c13,c82,c131]) ).
cnf(c525,plain,
multiply(X,multiply(commutator(Y,Z),commutator(Y,commutator(Z,X)))) = multiply(commutator(Y,Z),X),
inference(equational,[status(thm)],[c4,c27]) ).
cnf(c536,plain,
multiply(X,multiply(inverse(multiply(X,Y)),multiply(Z,Y))) = multiply(commutator(Y,X),multiply(Z,commutator(Z,Y))),
inference(equational,[status(thm)],[c27,c269]) ).
cnf(c537,plain,
multiply(commutator(X,Y),multiply(Z,commutator(Z,X))) = multiply(Z,commutator(multiply(inverse(Y),Z),X)),
inference(equational,[status(thm)],[c498,c536]) ).
cnf(c539,plain,
multiply(commutator(X,Y),multiply(Z,commutator(Y,Z))) = multiply(Z,commutator(Y,multiply(inverse(X),Z))),
inference(equational,[status(thm)],[c57,c65,c176,c537]) ).
cnf(c540,plain,
inverse(multiply(commutator(X,multiply(Y,Z)),Z)) = inverse(multiply(commutator(X,multiply(Z,Y)),Z)),
inference(equational,[status(thm)],[c3,c30,c38,c65,c120,c126,c439,c539]) ).
cnf(c541,plain,
commutator(multiply(X,Y),Z) = commutator(multiply(Y,X),Z),
inference(equational,[status(thm)],[c37,c52,c540]) ).
cnf(c545,plain,
commutator(X,multiply(Y,commutator(Y,Z))) = commutator(X,Y),
inference(equational,[status(thm)],[c37,c64,c193,c541]) ).
cnf(c571,plain,
multiply(X,multiply(commutator(Y,X),commutator(X,Z))) = multiply(Y,multiply(X,inverse(multiply(commutator(Z,X),Y)))),
inference(equational,[status(thm)],[c28,c66,c114,c140,c454]) ).
cnf(c572,plain,
multiply(commutator(X,Y),commutator(X,commutator(Y,Z))) = commutator(X,Y),
inference(equational,[status(thm)],[c1,c4,c5,c11,c28,c30,c33,c114,c126,c439,c545,c571]) ).
cnf(c574,plain,
multiply(X,commutator(Y,Z)) = multiply(commutator(Y,Z),X),
inference(equational,[status(thm)],[c525,c572]) ).
cnf(g1,plain,
multiply(a,commutator(b,c)) = multiply(commutator(b,c),a),
inference(equational,[status(thm)],[c574]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP024-5 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 08:05:34 EDT 2025
% 0.11/0.32 % CPUTime :
% 103.11/103.37 % SZS status Unsatisfiable
% 103.11/103.37 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------