%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP595-1 : TPTP v9.0.0. Released v2.6.0.
% 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 06:44:24 AM UTC 2025
% Result : Unsatisfiable 60.68s 61.09s
% Output : CNFRefutation 60.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% 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 : 110 ( 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,plain,
inverse(double_divide(X,Y)) = multiply(Y,X),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,axiom,
inverse(double_divide(double_divide(X,Y),inverse(double_divide(X,inverse(double_divide(Z,Y)))))) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c4,plain,
multiply(multiply(multiply(X,Y),Z),double_divide(Z,X)) = Y,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
multiply(X,double_divide(double_divide(Y,Z),multiply(Z,X))) = Y,
inference(equational,[status(thm)],[c4]) ).
cnf(c6,plain,
multiply(multiply(X,Y),double_divide(Y,Z)) = double_divide(double_divide(X,W),multiply(W,Z)),
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c7,plain,
multiply(X,multiply(multiply(Y,Z),double_divide(Z,X))) = Y,
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c8,plain,
double_divide(double_divide(multiply(X,Y),Z),multiply(Z,X)) = Y,
inference(equational,[status(thm)],[c4,c6]) ).
cnf(c10,plain,
inverse(multiply(multiply(X,Y),double_divide(Y,Z))) = multiply(multiply(W,Z),double_divide(X,W)),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c11,plain,
multiply(multiply(X,Y),double_divide(Z,X)) = multiply(multiply(W,Y),double_divide(Z,W)),
inference(equational,[status(thm)],[c2,c6,c10]) ).
cnf(c12,plain,
multiply(multiply(X,multiply(Y,double_divide(Z,X))),Z) = Y,
inference(equational,[status(thm)],[c5,c7]) ).
cnf(c14,plain,
multiply(multiply(X,Y),double_divide(Y,X)) = double_divide(double_divide(Z,W),multiply(W,Z)),
inference(equational,[status(thm)],[c6,c11]) ).
cnf(c15,plain,
multiply(multiply(X,Y),double_divide(multiply(Y,Z),X)) = inverse(Z),
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c16,plain,
double_divide(X,inverse(X)) = multiply(multiply(Y,Z),double_divide(Z,Y)),
inference(equational,[status(thm)],[c8,c14,c15]) ).
cnf(c18,plain,
multiply(X,double_divide(Y,inverse(Y))) = X,
inference(equational,[status(thm)],[c7,c16]) ).
cnf(c20,plain,
multiply(X,double_divide(Y,X)) = multiply(Z,double_divide(Y,Z)),
inference(equational,[status(thm)],[c11,c18]) ).
cnf(c21,plain,
multiply(X,double_divide(Y,X)) = inverse(Y),
inference(equational,[status(thm)],[c18,c20]) ).
cnf(c24,plain,
multiply(inverse(X),multiply(Y,X)) = Y,
inference(equational,[status(thm)],[c7,c18]) ).
cnf(c25,plain,
multiply(multiply(inverse(X),Y),X) = Y,
inference(equational,[status(thm)],[c12,c18]) ).
cnf(c27,plain,
multiply(inverse(X),Y) = double_divide(X,inverse(Y)),
inference(equational,[status(thm)],[c20,c21,c25]) ).
cnf(c29,plain,
multiply(double_divide(X,inverse(Y)),X) = Y,
inference(equational,[status(thm)],[c4,c18,c27]) ).
cnf(c30,plain,
double_divide(multiply(X,Y),inverse(X)) = inverse(Y),
inference(equational,[status(thm)],[c15,c18,c27]) ).
cnf(c31,plain,
double_divide(inverse(X),inverse(Y)) = multiply(Y,X),
inference(equational,[status(thm)],[c2,c20,c21,c30]) ).
cnf(c33,plain,
double_divide(X,inverse(inverse(Y))) = inverse(multiply(X,Y)),
inference(equational,[status(thm)],[c24,c30]) ).
cnf(c35,plain,
multiply(multiply(X,Y),Z) = multiply(multiply(X,Z),Y),
inference(equational,[status(thm)],[c2,c12,c25]) ).
cnf(c36,plain,
multiply(multiply(X,Y),inverse(Y)) = X,
inference(equational,[status(thm)],[c2,c20,c21,c24]) ).
cnf(c37,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c25,c36]) ).
cnf(c38,plain,
multiply(X,Y) = multiply(Y,X),
inference(equational,[status(thm)],[c27,c31,c37]) ).
cnf(c39,plain,
multiply(X,inverse(Y)) = double_divide(Y,inverse(X)),
inference(equational,[status(thm)],[c29,c36]) ).
cnf(c40,plain,
double_divide(X,Y) = double_divide(Y,X),
inference(equational,[status(thm)],[c27,c37,c39]) ).
cnf(c41,plain,
inverse(multiply(X,Y)) = double_divide(X,Y),
inference(equational,[status(thm)],[c33,c37]) ).
cnf(c43,plain,
multiply(double_divide(X,inverse(Y)),multiply(Z,X)) = multiply(Y,Z),
inference(equational,[status(thm)],[c12,c15,c39]) ).
cnf(c49,plain,
multiply(X,multiply(double_divide(Y,Z),multiply(Z,Y))) = X,
inference(equational,[status(thm)],[c7,c11,c38]) ).
cnf(c50,plain,
double_divide(multiply(X,Y),inverse(Z)) = multiply(Z,double_divide(Y,X)),
inference(equational,[status(thm)],[c43,c49]) ).
cnf(c52,plain,
multiply(multiply(X,Y),double_divide(Y,multiply(multiply(Z,X),W))) = double_divide(W,Z),
inference(equational,[status(thm)],[c4]) ).
cnf(c53,plain,
double_divide(X,multiply(Y,double_divide(Z,multiply(X,Y)))) = Z,
inference(equational,[status(thm)],[c5,c40,c52]) ).
cnf(c56,plain,
multiply(multiply(X,Y),double_divide(Z,multiply(Y,X))) = inverse(Z),
inference(equational,[status(thm)],[c2,c35,c53]) ).
cnf(c57,plain,
multiply(multiply(X,Y),Z) = multiply(Y,multiply(X,Z)),
inference(equational,[status(thm)],[c2,c8,c56]) ).
cnf(c58,plain,
double_divide(X,multiply(Y,double_divide(X,Z))) = double_divide(Y,inverse(Z)),
inference(equational,[status(thm)],[c10,c21,c39,c41,c57]) ).
cnf(c60,plain,
multiply(X,double_divide(multiply(X,Y),Z)) = double_divide(Y,Z),
inference(equational,[status(thm)],[c4,c50,c57,c58]) ).
cnf(c62,plain,
multiply(X,multiply(Y,Z)) = multiply(Y,multiply(X,Z)),
inference(equational,[status(thm)],[c2,c15,c21,c57,c60]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c38,c62]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP595-1 : TPTP v9.0.0. Released v2.6.0.
% 0.06/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n012.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 08:33:19 EDT 2025
% 0.11/0.32 % CPUTime :
% 60.68/61.09 % SZS status Unsatisfiable
% 60.68/61.09 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------