%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP615-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n015.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 06:44:27 AM UTC 2025
% Result : Unsatisfiable 1.95s 2.14s
% Output : CNFRefutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% 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 : 11 ( 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 : 61 ( 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(inverse(double_divide(X,inverse(Y))),Z)),double_divide(X,Z)) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
double_divide(inverse(X),double_divide(inverse(double_divide(Y,inverse(X))),double_divide(Y,inverse(Z)))) = Z,
inference(equational,[status(thm)],[c2]) ).
cnf(c5,plain,
double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(inverse(double_divide(X,inverse(Y))),Z)),inverse(W))),double_divide(X,Z))),Y) = W,
inference(equational,[status(thm)],[c2]) ).
cnf(c6,plain,
double_divide(inverse(double_divide(inverse(X),inverse(Y))),X) = Y,
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,plain,
double_divide(inverse(X),double_divide(inverse(Y),Y)) = X,
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c8,plain,
double_divide(inverse(double_divide(inverse(X),X)),inverse(Y)) = Y,
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c9,plain,
double_divide(inverse(X),double_divide(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c11,plain,
double_divide(inverse(double_divide(inverse(X),X)),Y) = inverse(Y),
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c12,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c6,c11]) ).
cnf(c23,plain,
double_divide(inverse(X),double_divide(Y,inverse(X))) = Y,
inference(equational,[status(thm)],[c6,c12]) ).
cnf(c24,plain,
double_divide(inverse(X),Y) = double_divide(Y,inverse(X)),
inference(equational,[status(thm)],[c3,c23]) ).
cnf(c25,plain,
inverse(double_divide(X,inverse(Y))) = double_divide(inverse(X),Y),
inference(equational,[status(thm)],[c6,c12,c23]) ).
cnf(c26,plain,
double_divide(X,Y) = double_divide(Y,X),
inference(equational,[status(thm)],[c12,c24,c25]) ).
cnf(c27,plain,
double_divide(X,double_divide(Y,X)) = Y,
inference(equational,[status(thm)],[c6,c12,c25,c26]) ).
cnf(c28,plain,
inverse(double_divide(inverse(X),Y)) = double_divide(inverse(Y),X),
inference(equational,[status(thm)],[c24,c25]) ).
cnf(c29,plain,
inverse(X) = double_divide(X,double_divide(Y,inverse(Y))),
inference(equational,[status(thm)],[c8,c12,c24,c28]) ).
cnf(c41,plain,
double_divide(double_divide(X,Y),Z) = double_divide(double_divide(X,inverse(X)),double_divide(double_divide(inverse(X),Z),Y)),
inference(equational,[status(thm)],[c2,c25,c26,c27,c29]) ).
cnf(c43,plain,
double_divide(double_divide(inverse(X),Y),double_divide(Z,inverse(Z))) = double_divide(X,inverse(Y)),
inference(equational,[status(thm)],[c7,c24,c25]) ).
cnf(c44,plain,
double_divide(double_divide(X,Y),double_divide(Z,inverse(Z))) = double_divide(inverse(Y),inverse(X)),
inference(equational,[status(thm)],[c12,c24,c43]) ).
cnf(c50,plain,
double_divide(inverse(X),inverse(Y)) = double_divide(double_divide(Z,inverse(Z)),double_divide(Y,X)),
inference(equational,[status(thm)],[c26,c44]) ).
cnf(c51,plain,
double_divide(inverse(X),double_divide(inverse(Y),Z)) = double_divide(double_divide(Z,X),Y),
inference(equational,[status(thm)],[c28,c41,c50]) ).
cnf(c56,plain,
double_divide(inverse(X),double_divide(Y,Z)) = double_divide(double_divide(Z,X),inverse(Y)),
inference(equational,[status(thm)],[c12,c51]) ).
cnf(c57,plain,
double_divide(inverse(X),double_divide(Y,Z)) = double_divide(inverse(Y),double_divide(Z,X)),
inference(equational,[status(thm)],[c12,c24,c51]) ).
cnf(c66,plain,
double_divide(inverse(X),double_divide(Y,Z)) = double_divide(inverse(Y),double_divide(X,Z)),
inference(equational,[status(thm)],[c26,c57]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c1,c24,c25,c26,c28,c56,c66]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP615-1 : TPTP v9.0.0. Released v2.6.0.
% 0.06/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n015.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 08:33:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.95/2.14 % SZS status Unsatisfiable
% 1.95/2.14 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------