%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP002-4 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n005.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 06:43:15 AM UTC 2025
% Result : Unsatisfiable 29.89s 30.05s
% Output : CNFRefutation 29.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 3 RR)
% Number of literals : 31 ( 30 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 : 53 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
commutator(commutator(a,b),b) != identity,
file('theBenchmark.p',prove_commutator) ).
cnf(c1,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c2,axiom,
multiply(X,identity) = X,
file('theBenchmark.p',right_identity) ).
cnf(c3,axiom,
multiply(X,inverse(X)) = identity,
file('theBenchmark.p',right_inverse) ).
cnf(c5,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c6,axiom,
multiply(X,multiply(X,X)) = identity,
file('theBenchmark.p',x_cubed_is_identity) ).
cnf(c7,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c8,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c1,c3,c7]) ).
cnf(c9,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c2,c3,c8]) ).
cnf(c10,plain,
multiply(inverse(X),inverse(X)) = X,
inference(equational,[status(thm)],[c2,c6,c8]) ).
cnf(c11,plain,
multiply(X,X) = inverse(X),
inference(equational,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c1,c5,c7]) ).
cnf(c13,plain,
multiply(X,multiply(X,multiply(X,Y))) = Y,
inference(equational,[status(thm)],[c1,c6,c7]) ).
cnf(c14,plain,
multiply(inverse(X),Y) = multiply(X,multiply(X,Y)),
inference(equational,[status(thm)],[c12,c13]) ).
cnf(c15,plain,
multiply(X,multiply(Y,inverse(multiply(X,Y)))) = identity,
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c16,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(equational,[status(thm)],[c2,c11,c13,c15]) ).
cnf(c17,plain,
multiply(X,inverse(Y)) = inverse(multiply(Y,inverse(X))),
inference(equational,[status(thm)],[c8,c16]) ).
cnf(c18,plain,
multiply(X,multiply(X,inverse(Y))) = inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c13,c16]) ).
cnf(c19,plain,
multiply(X,inverse(multiply(Y,multiply(Y,X)))) = Y,
inference(equational,[status(thm)],[c2,c8,c14,c15]) ).
cnf(c21,plain,
multiply(X,Y) = inverse(multiply(Y,multiply(Y,inverse(X)))),
inference(equational,[status(thm)],[c8,c19]) ).
cnf(c22,axiom,
commutator(X,Y) = multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))),
file('theBenchmark.p',commutator) ).
cnf(c23,plain,
commutator(X,Y) = multiply(X,multiply(Y,multiply(X,multiply(X,inverse(Y))))),
inference(equational,[status(thm)],[c14,c22]) ).
cnf(c24,plain,
multiply(X,multiply(Y,multiply(X,Y))) = inverse(multiply(X,Y)),
inference(equational,[status(thm)],[c7,c11]) ).
cnf(c25,plain,
multiply(X,inverse(multiply(Y,inverse(X)))) = inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c12,c14,c18,c21]) ).
cnf(c27,plain,
multiply(X,inverse(multiply(Y,multiply(Z,X)))) = inverse(multiply(Y,Z)),
inference(equational,[status(thm)],[c7,c16]) ).
cnf(c29,plain,
inverse(multiply(X,inverse(multiply(Y,Z)))) = multiply(Y,multiply(Z,inverse(X))),
inference(equational,[status(thm)],[c7,c17]) ).
cnf(c31,plain,
multiply(X,inverse(multiply(Y,inverse(Z)))) = inverse(multiply(Y,inverse(multiply(X,Z)))),
inference(equational,[status(thm)],[c17,c29]) ).
cnf(c42,plain,
multiply(X,inverse(multiply(X,multiply(X,Y)))) = multiply(Y,multiply(X,multiply(X,Y))),
inference(equational,[status(thm)],[c8,c14,c24]) ).
cnf(c55,plain,
multiply(X,multiply(X,multiply(Y,multiply(Y,Z)))) = multiply(Y,multiply(X,multiply(Y,multiply(X,Z)))),
inference(equational,[status(thm)],[c7,c14,c18]) ).
cnf(g1,plain,
commutator(commutator(a,b),b) = identity,
inference(equational,[status(thm)],[c3,c7,c9,c10,c11,c12,c13,c14,c16,c17,c23,c25,c27,c31,c42,c55]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP002-4 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n005.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 08:04:34 EDT 2025
% 0.11/0.33 % CPUTime :
% 29.89/30.05 % SZS status Unsatisfiable
% 29.89/30.05 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------