%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP002-3 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n012.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 3.71s 3.90s
% Output : CNFRefutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 3 RR)
% Number of literals : 28 ( 27 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 46 ( 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(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c3,axiom,
multiply(X,multiply(X,X)) = identity,
file('theBenchmark.p',x_cubed_is_identity) ).
cnf(c4,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c5,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c1,c2,c4]) ).
cnf(c8,plain,
multiply(inverse(X),identity) = multiply(X,X),
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c9,plain,
multiply(inverse(X),inverse(X)) = X,
inference(equational,[status(thm)],[c2,c5,c8]) ).
cnf(c10,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c5]) ).
cnf(c11,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c8,c9,c10]) ).
cnf(c12,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c10,c11]) ).
cnf(c13,plain,
multiply(X,X) = inverse(X),
inference(equational,[status(thm)],[c8,c11]) ).
cnf(c14,plain,
multiply(X,inverse(X)) = identity,
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c15,plain,
multiply(X,multiply(X,multiply(X,Y))) = Y,
inference(equational,[status(thm)],[c1,c3,c4]) ).
cnf(c16,plain,
multiply(inverse(X),Y) = multiply(X,multiply(X,Y)),
inference(equational,[status(thm)],[c5,c15]) ).
cnf(c17,axiom,
commutator(X,Y) = multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))),
file('theBenchmark.p',commutator) ).
cnf(c18,plain,
commutator(X,Y) = multiply(X,multiply(Y,multiply(X,multiply(X,inverse(Y))))),
inference(equational,[status(thm)],[c16,c17]) ).
cnf(c19,plain,
multiply(X,multiply(Y,inverse(multiply(X,Y)))) = identity,
inference(equational,[status(thm)],[c4,c14]) ).
cnf(c20,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(equational,[status(thm)],[c11,c13,c15,c19]) ).
cnf(c23,plain,
multiply(X,multiply(Y,multiply(X,Y))) = inverse(multiply(X,Y)),
inference(equational,[status(thm)],[c4,c13]) ).
cnf(c24,plain,
multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,multiply(Y,Z)))))) = Z,
inference(equational,[status(thm)],[c4,c5,c16]) ).
cnf(c28,plain,
multiply(X,inverse(multiply(Y,multiply(Z,X)))) = inverse(multiply(Y,Z)),
inference(equational,[status(thm)],[c4,c20]) ).
cnf(c31,plain,
multiply(X,multiply(X,inverse(multiply(X,Y)))) = multiply(Y,multiply(X,Y)),
inference(equational,[status(thm)],[c5,c16,c23]) ).
cnf(c35,plain,
multiply(X,multiply(Y,multiply(X,multiply(Y,multiply(X,Z))))) = multiply(Y,multiply(Y,Z)),
inference(equational,[status(thm)],[c15,c24]) ).
cnf(c36,plain,
multiply(X,multiply(Y,multiply(X,multiply(Y,Z)))) = multiply(Y,multiply(Y,multiply(X,multiply(X,Z)))),
inference(equational,[status(thm)],[c15,c35]) ).
cnf(c42,plain,
multiply(X,multiply(Y,multiply(Y,X))) = multiply(Y,inverse(multiply(Y,multiply(Y,X)))),
inference(equational,[status(thm)],[c15,c16,c31]) ).
cnf(g1,plain,
commutator(commutator(a,b),b) = identity,
inference(equational,[status(thm)],[c4,c5,c9,c11,c12,c13,c14,c15,c16,c18,c20,c28,c31,c36,c42]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP002-3 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 08:04:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 3.71/3.90 % SZS status Unsatisfiable
% 3.71/3.90 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------