%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP607-1 : TPTP v9.0.0. Released v2.6.0.
% 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 06:44:26 AM UTC 2025
% Result : Unsatisfiable 1.09s 1.27s
% Output : CNFRefutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of clauses : 44 ( 44 unt; 0 nHn; 3 RR)
% Number of literals : 44 ( 43 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 : 109 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('theBenchmark.p',prove_these_axioms_3) ).
cnf(c1,axiom,
multiply(X,Y) = inverse(double_divide(Y,X)),
file('theBenchmark.p',multiply) ).
cnf(c2,axiom,
double_divide(inverse(double_divide(X,inverse(double_divide(inverse(Y),double_divide(X,Z))))),Z) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
double_divide(inverse(double_divide(X,inverse(Y))),Z) = double_divide(W,inverse(double_divide(inverse(Y),double_divide(W,double_divide(X,Z))))),
inference(equational,[status(thm)],[c2]) ).
cnf(c4,plain,
double_divide(inverse(double_divide(inverse(double_divide(X,inverse(Y))),Z)),double_divide(X,Z)) = Y,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
double_divide(inverse(X),double_divide(inverse(double_divide(Y,inverse(X))),double_divide(Y,inverse(Z)))) = Z,
inference(equational,[status(thm)],[c4]) ).
cnf(c6,plain,
double_divide(inverse(double_divide(inverse(X),double_divide(Y,double_divide(Y,inverse(Z))))),X) = Z,
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,plain,
double_divide(inverse(double_divide(X,inverse(Y))),Z) = double_divide(inverse(double_divide(X,Z)),double_divide(W,double_divide(W,inverse(Y)))),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c8,plain,
double_divide(X,inverse(double_divide(inverse(double_divide(Y,inverse(Z))),W))) = double_divide(inverse(double_divide(X,inverse(double_divide(Y,W)))),inverse(Z)),
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c9,plain,
double_divide(inverse(double_divide(X,Y)),double_divide(Z,double_divide(Z,inverse(W)))) = double_divide(V,inverse(double_divide(inverse(W),double_divide(V,double_divide(X,Y))))),
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c10,plain,
double_divide(X,inverse(double_divide(inverse(Y),double_divide(X,Z)))) = double_divide(inverse(Z),double_divide(W,double_divide(W,inverse(Y)))),
inference(equational,[status(thm)],[c6,c9]) ).
cnf(c15,plain,
double_divide(inverse(X),inverse(double_divide(inverse(Y),Z))) = double_divide(inverse(double_divide(inverse(double_divide(W,inverse(X))),inverse(Y))),double_divide(W,inverse(Z))),
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c16,plain,
double_divide(inverse(X),inverse(double_divide(inverse(Y),Y))) = X,
inference(equational,[status(thm)],[c4,c15]) ).
cnf(c17,plain,
double_divide(inverse(double_divide(inverse(X),inverse(Y))),X) = Y,
inference(equational,[status(thm)],[c4,c16]) ).
cnf(c18,plain,
double_divide(inverse(X),X) = double_divide(inverse(Y),Y),
inference(equational,[status(thm)],[c16,c17]) ).
cnf(c19,plain,
double_divide(inverse(X),X) = inverse(double_divide(inverse(Y),Y)),
inference(equational,[status(thm)],[c16,c18]) ).
cnf(c21,plain,
double_divide(inverse(X),inverse(double_divide(inverse(Y),X))) = Y,
inference(equational,[status(thm)],[c2,c16]) ).
cnf(c23,plain,
double_divide(double_divide(inverse(X),X),inverse(Y)) = Y,
inference(equational,[status(thm)],[c17,c19]) ).
cnf(c24,plain,
double_divide(inverse(double_divide(X,Y)),inverse(Z)) = double_divide(inverse(double_divide(X,inverse(Z))),Y),
inference(equational,[status(thm)],[c4,c21]) ).
cnf(c25,plain,
double_divide(inverse(X),inverse(Y)) = double_divide(inverse(Y),inverse(X)),
inference(equational,[status(thm)],[c23,c24]) ).
cnf(c26,plain,
double_divide(inverse(X),inverse(inverse(double_divide(inverse(Y),Y)))) = X,
inference(equational,[status(thm)],[c16]) ).
cnf(c29,plain,
double_divide(inverse(double_divide(inverse(X),X)),inverse(Y)) = Y,
inference(equational,[status(thm)],[c17,c24]) ).
cnf(c30,plain,
double_divide(inverse(X),inverse(inverse(X))) = double_divide(inverse(Y),Y),
inference(equational,[status(thm)],[c21,c25,c29]) ).
cnf(c31,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c16,c21,c30]) ).
cnf(c33,plain,
double_divide(X,inverse(Y)) = double_divide(inverse(Y),X),
inference(equational,[status(thm)],[c25,c31]) ).
cnf(c34,plain,
double_divide(X,Y) = double_divide(Y,X),
inference(equational,[status(thm)],[c31,c33]) ).
cnf(c37,plain,
double_divide(inverse(X),double_divide(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c5,c29]) ).
cnf(c38,plain,
double_divide(X,double_divide(X,Y)) = Y,
inference(equational,[status(thm)],[c31,c37]) ).
cnf(c39,plain,
inverse(double_divide(inverse(X),Y)) = double_divide(inverse(Y),X),
inference(equational,[status(thm)],[c21,c37]) ).
cnf(c40,plain,
inverse(double_divide(X,Y)) = double_divide(inverse(Y),inverse(X)),
inference(equational,[status(thm)],[c31,c39]) ).
cnf(c44,plain,
double_divide(double_divide(X,inverse(X)),inverse(Y)) = Y,
inference(equational,[status(thm)],[c17,c18,c24,c31,c33,c40]) ).
cnf(c46,plain,
double_divide(double_divide(X,Y),Z) = double_divide(inverse(Y),double_divide(inverse(Z),X)),
inference(equational,[status(thm)],[c15,c31,c39,c44]) ).
cnf(c48,plain,
double_divide(double_divide(X,inverse(Y)),inverse(Z)) = double_divide(Y,double_divide(X,Z)),
inference(equational,[status(thm)],[c8,c31,c39,c40,c44]) ).
cnf(c50,plain,
double_divide(X,double_divide(double_divide(inverse(Y),inverse(X)),Z)) = double_divide(inverse(Y),inverse(Z)),
inference(equational,[status(thm)],[c3,c16,c39,c40]) ).
cnf(c51,plain,
double_divide(double_divide(X,inverse(X)),double_divide(Y,Z)) = double_divide(inverse(Y),inverse(Z)),
inference(equational,[status(thm)],[c26,c33,c39,c50]) ).
cnf(c52,plain,
double_divide(double_divide(X,inverse(X)),Y) = double_divide(Y,double_divide(Z,inverse(Z))),
inference(equational,[status(thm)],[c17,c31,c33,c39,c40,c48,c51]) ).
cnf(c53,plain,
double_divide(inverse(X),double_divide(Y,inverse(Y))) = X,
inference(equational,[status(thm)],[c5,c37,c38,c48,c52]) ).
cnf(c56,plain,
double_divide(X,double_divide(double_divide(Y,inverse(Y)),Z)) = double_divide(X,inverse(Z)),
inference(equational,[status(thm)],[c18,c31,c33,c50]) ).
cnf(c57,plain,
double_divide(double_divide(X,Y),inverse(Z)) = double_divide(inverse(Y),double_divide(Z,X)),
inference(equational,[status(thm)],[c31,c40,c46,c53,c56]) ).
cnf(c60,plain,
double_divide(double_divide(inverse(X),Y),double_divide(Z,X)) = double_divide(inverse(Z),inverse(Y)),
inference(equational,[status(thm)],[c10,c31,c38,c39,c50]) ).
cnf(c61,plain,
double_divide(X,double_divide(Y,Z)) = double_divide(inverse(Y),double_divide(inverse(X),Z)),
inference(equational,[status(thm)],[c21,c39,c60]) ).
cnf(c63,plain,
double_divide(inverse(X),double_divide(Y,Z)) = double_divide(inverse(Y),double_divide(X,Z)),
inference(equational,[status(thm)],[c31,c61]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c1,c25,c31,c33,c34,c39,c40,c57,c63]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP607-1 : TPTP v9.0.0. Released v2.6.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n005.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 08:33:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.09/1.27 % SZS status Unsatisfiable
% 1.09/1.27 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------