%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP591-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n002.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 06:44:24 AM UTC 2025
% Result : Unsatisfiable 1.07s 1.23s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 3 RR)
% Number of literals : 27 ( 26 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 : 58 ( 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(double_divide(X,Y),inverse(double_divide(X,inverse(Z))))),Y) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
double_divide(inverse(double_divide(X,inverse(double_divide(inverse(double_divide(double_divide(Y,Z),inverse(double_divide(Y,inverse(X))))),inverse(W))))),Z) = W,
inference(equational,[status(thm)],[c2]) ).
cnf(c4,plain,
double_divide(inverse(double_divide(X,inverse(X))),inverse(Y)) = Y,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
double_divide(inverse(double_divide(X,inverse(Y))),inverse(X)) = Y,
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c7,plain,
double_divide(inverse(X),inverse(inverse(double_divide(Y,inverse(X))))) = Y,
inference(equational,[status(thm)],[c5]) ).
cnf(c8,plain,
inverse(double_divide(X,inverse(Y))) = double_divide(inverse(X),inverse(inverse(Y))),
inference(equational,[status(thm)],[c5,c7]) ).
cnf(c9,plain,
double_divide(inverse(X),inverse(inverse(X))) = double_divide(inverse(Y),inverse(inverse(Y))),
inference(equational,[status(thm)],[c4,c7,c8]) ).
cnf(c10,plain,
inverse(double_divide(X,double_divide(inverse(Y),inverse(inverse(Y))))) = X,
inference(equational,[status(thm)],[c4,c7,c8]) ).
cnf(c11,plain,
inverse(double_divide(X,Y)) = double_divide(inverse(X),inverse(Y)),
inference(equational,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
double_divide(X,inverse(X)) = double_divide(inverse(Y),inverse(inverse(Y))),
inference(equational,[status(thm)],[c9,c10]) ).
cnf(c14,plain,
double_divide(double_divide(X,Y),Y) = X,
inference(equational,[status(thm)],[c2,c8,c10,c12]) ).
cnf(c16,plain,
double_divide(double_divide(X,inverse(inverse(Y))),X) = Y,
inference(equational,[status(thm)],[c5,c8,c10]) ).
cnf(c17,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c14,c16]) ).
cnf(c20,plain,
double_divide(double_divide(X,Y),X) = Y,
inference(equational,[status(thm)],[c5,c8,c17]) ).
cnf(c21,plain,
double_divide(X,Y) = double_divide(Y,X),
inference(equational,[status(thm)],[c14,c20]) ).
cnf(c30,plain,
double_divide(X,double_divide(double_divide(Y,inverse(X)),Z)) = double_divide(inverse(Z),Y),
inference(equational,[status(thm)],[c2,c7,c8,c11,c17,c21]) ).
cnf(c31,plain,
double_divide(X,double_divide(Y,Z)) = double_divide(inverse(Z),double_divide(inverse(X),Y)),
inference(equational,[status(thm)],[c5,c8,c17,c30]) ).
cnf(c34,plain,
double_divide(double_divide(inverse(X),Y),double_divide(X,Z)) = double_divide(inverse(Z),inverse(Y)),
inference(equational,[status(thm)],[c7,c8,c17,c30]) ).
cnf(c35,plain,
double_divide(double_divide(X,Y),Z) = double_divide(double_divide(inverse(Z),X),inverse(Y)),
inference(equational,[status(thm)],[c7,c8,c11,c17,c34]) ).
cnf(c36,plain,
double_divide(inverse(X),double_divide(Y,Z)) = double_divide(inverse(Y),double_divide(Z,X)),
inference(equational,[status(thm)],[c17,c31]) ).
cnf(c38,plain,
double_divide(double_divide(X,Y),inverse(Z)) = double_divide(double_divide(Y,Z),inverse(X)),
inference(equational,[status(thm)],[c17,c35]) ).
cnf(c39,plain,
double_divide(X,double_divide(Y,Z)) = double_divide(inverse(Z),double_divide(Y,inverse(X))),
inference(equational,[status(thm)],[c14,c30]) ).
cnf(c58,plain,
double_divide(inverse(X),double_divide(Y,Z)) = double_divide(inverse(Y),double_divide(X,Z)),
inference(equational,[status(thm)],[c17,c36,c39]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c1,c8,c11,c17,c21,c38,c58]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP591-1 : TPTP v9.0.0. Released v2.6.0.
% 0.08/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n002.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
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 08:33:34 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.07/1.23 % SZS status Unsatisfiable
% 1.07/1.23 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------