%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP423-1 : 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 06:44:01 AM UTC 2025
% Result : Unsatisfiable 83.08s 83.19s
% Output : CNFRefutation 83.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of clauses : 86 ( 86 unt; 0 nHn; 3 RR)
% Number of literals : 86 ( 85 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 272 ( 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,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))))),multiply(X,Z))) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(Y,multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))))),multiply(X,Z))) = multiply(inverse(multiply(W,inverse(multiply(inverse(Y),multiply(inverse(V),inverse(multiply(inverse(V),V))))))),multiply(W,V)),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
inverse(inverse(multiply(inverse(multiply(X,inverse(multiply(Y,multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))))),multiply(X,Z)))) = Y,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))))),multiply(X,Z)) = Y,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c6,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(Y,multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))))),multiply(X,Z))) = inverse(multiply(inverse(multiply(W,inverse(multiply(Y,multiply(inverse(V),inverse(multiply(inverse(V),V))))))),multiply(W,V))),
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c7,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))) = multiply(inverse(Z),inverse(multiply(inverse(Y),multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z)))))))),
inference(equational,[status(thm)],[c1]) ).
cnf(c8,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z)))),multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))) = Y,
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c9,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(multiply(W,Y)),multiply(W,Z)),
inference(equational,[status(thm)],[c4,c8]) ).
cnf(c10,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))) = inverse(multiply(inverse(multiply(W,Y)),multiply(W,Z))),
inference(equational,[status(thm)],[c2,c4,c8]) ).
cnf(c11,plain,
inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z)))) = inverse(inverse(multiply(inverse(multiply(W,Y)),multiply(W,Z)))),
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c12,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(W,Y)),V)) = multiply(inverse(multiply(U,multiply(W,Z))),multiply(U,V)),
inference(equational,[status(thm)],[c9,c10]) ).
cnf(c16,plain,
multiply(X,multiply(inverse(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,Z)))),W)) = multiply(inverse(multiply(V,multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))),multiply(V,W)),
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c21,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),multiply(inverse(Z),inverse(multiply(inverse(Z),Z)))) = Y,
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c22,plain,
inverse(multiply(X,multiply(inverse(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,Z)))),W))) = inverse(multiply(inverse(multiply(V,multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))),multiply(V,W))),
inference(equational,[status(thm)],[c8,c10]) ).
cnf(c23,plain,
inverse(multiply(X,multiply(inverse(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,Z)))),W))) = inverse(multiply(V,multiply(inverse(inverse(multiply(inverse(multiply(U,V)),multiply(U,Z)))),W))),
inference(equational,[status(thm)],[c16,c22]) ).
cnf(c24,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),W)),Y) = multiply(inverse(multiply(V,W)),multiply(V,multiply(inverse(Z),inverse(multiply(inverse(Z),Z))))),
inference(equational,[status(thm)],[c9,c21]) ).
cnf(c26,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),W)),Y) = multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(V,inverse(U))),multiply(V,Z)))),W)),U),
inference(equational,[status(thm)],[c21,c24]) ).
cnf(c27,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c8,c21,c26]) ).
cnf(c28,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(Y),Y)),
inference(equational,[status(thm)],[c10,c27]) ).
cnf(c29,plain,
inverse(inverse(multiply(inverse(X),X))) = inverse(inverse(multiply(inverse(Y),Y))),
inference(equational,[status(thm)],[c11,c27]) ).
cnf(c30,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)) = multiply(inverse(Z),Z),
inference(equational,[status(thm)],[c27,c28]) ).
cnf(c31,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(W,Y)),multiply(W,X)),
inference(equational,[status(thm)],[c9,c27]) ).
cnf(c32,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(multiply(W,Y)),multiply(W,Z)),
inference(equational,[status(thm)],[c9,c27]) ).
cnf(c33,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y))) = inverse(multiply(inverse(Z),Z)),
inference(equational,[status(thm)],[c28]) ).
cnf(c34,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(W),W)),
inference(equational,[status(thm)],[c27,c31]) ).
cnf(c35,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(X,multiply(inverse(Z),Z)),
inference(equational,[status(thm)],[c1,c34]) ).
cnf(c36,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(multiply(inverse(Z),Y)),multiply(inverse(W),W)),
inference(equational,[status(thm)],[c28,c31]) ).
cnf(c38,plain,
inverse(multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z))) = inverse(multiply(inverse(multiply(W,Y)),multiply(W,X))),
inference(equational,[status(thm)],[c10,c27]) ).
cnf(c39,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),Y))) = multiply(inverse(Z),Z),
inference(equational,[status(thm)],[c27,c29]) ).
cnf(c40,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)) = multiply(inverse(multiply(inverse(Z),Z)),multiply(inverse(W),W)),
inference(equational,[status(thm)],[c30,c32]) ).
cnf(c41,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(multiply(inverse(W),W)),multiply(inverse(Y),Z)),
inference(equational,[status(thm)],[c32,c36]) ).
cnf(c42,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = multiply(inverse(multiply(inverse(Z),Z)),Y),
inference(equational,[status(thm)],[c21,c41]) ).
cnf(c46,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z))) = inverse(multiply(inverse(multiply(inverse(Z),Y)),multiply(inverse(W),W))),
inference(equational,[status(thm)],[c28,c38]) ).
cnf(c47,plain,
inverse(multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z))) = inverse(multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(W),W))),
inference(equational,[status(thm)],[c27,c38]) ).
cnf(c48,plain,
inverse(multiply(X,multiply(inverse(Y),Y))) = inverse(multiply(X,multiply(inverse(Z),Z))),
inference(equational,[status(thm)],[c8,c47]) ).
cnf(c49,plain,
multiply(inverse(X),inverse(multiply(inverse(Y),multiply(inverse(Z),Z)))) = inverse(multiply(inverse(multiply(W,Y)),multiply(W,X))),
inference(equational,[status(thm)],[c7,c39]) ).
cnf(c50,plain,
multiply(inverse(X),inverse(multiply(inverse(X),multiply(inverse(Y),Y)))) = inverse(multiply(inverse(Z),Z)),
inference(equational,[status(thm)],[c33,c49]) ).
cnf(c51,plain,
multiply(X,inverse(multiply(X,multiply(inverse(Y),Y)))) = inverse(multiply(inverse(Z),Z)),
inference(equational,[status(thm)],[c3,c50]) ).
cnf(c57,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),multiply(X,Z))) = multiply(inverse(Z),inverse(multiply(inverse(Z),Z))),
inference(equational,[status(thm)],[c1,c6,c27]) ).
cnf(c58,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),Y)))) = inverse(multiply(inverse(Z),Z)),
inference(equational,[status(thm)],[c28,c29]) ).
cnf(c61,plain,
multiply(inverse(multiply(X,Y)),multiply(X,multiply(inverse(Z),Z))) = multiply(inverse(multiply(W,Y)),multiply(W,multiply(inverse(V),V))),
inference(equational,[status(thm)],[c9,c35]) ).
cnf(c62,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z))) = multiply(inverse(Z),inverse(multiply(inverse(Y),multiply(inverse(W),W)))),
inference(equational,[status(thm)],[c27,c49]) ).
cnf(c63,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(Y,Z))) = multiply(inverse(Z),inverse(multiply(Y,multiply(inverse(W),W)))),
inference(equational,[status(thm)],[c3,c62]) ).
cnf(c66,plain,
multiply(inverse(X),inverse(multiply(inverse(Y),Y))) = inverse(multiply(inverse(multiply(Z,inverse(multiply(inverse(W),W)))),multiply(Z,X))),
inference(equational,[status(thm)],[c28,c57]) ).
cnf(c73,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),Y))) = inverse(multiply(inverse(Z),Z)),
inference(equational,[status(thm)],[c28,c66]) ).
cnf(c74,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c39,c73]) ).
cnf(c75,plain,
inverse(inverse(multiply(inverse(X),X))) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c58,c73,c74]) ).
cnf(c76,plain,
inverse(inverse(multiply(inverse(X),X))) = inverse(multiply(inverse(Y),Y)),
inference(equational,[status(thm)],[c28,c73]) ).
cnf(c78,plain,
inverse(inverse(inverse(multiply(inverse(X),X)))) = inverse(inverse(multiply(inverse(Y),Y))),
inference(equational,[status(thm)],[c29,c73]) ).
cnf(c80,plain,
inverse(inverse(inverse(multiply(inverse(X),X)))) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c75,c78]) ).
cnf(c85,plain,
inverse(multiply(X,inverse(multiply(inverse(Y),Y)))) = inverse(multiply(X,multiply(inverse(Z),Z))),
inference(equational,[status(thm)],[c48,c73]) ).
cnf(c106,plain,
inverse(multiply(X,inverse(inverse(multiply(inverse(Y),Y))))) = inverse(multiply(X,multiply(inverse(Z),Z))),
inference(equational,[status(thm)],[c48,c75]) ).
cnf(c112,plain,
inverse(inverse(multiply(inverse(X),X))) = multiply(Y,inverse(multiply(Y,multiply(inverse(Z),Z)))),
inference(equational,[status(thm)],[c51,c76]) ).
cnf(c115,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)) = inverse(multiply(inverse(Z),Z)),
inference(equational,[status(thm)],[c28,c74]) ).
cnf(c119,plain,
multiply(multiply(inverse(X),X),multiply(inverse(Y),Y)) = inverse(inverse(inverse(multiply(inverse(Z),Z)))),
inference(equational,[status(thm)],[c74,c80]) ).
cnf(c156,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),multiply(inverse(Y),Z)) = multiply(inverse(multiply(W,Y)),multiply(W,Z)),
inference(equational,[status(thm)],[c32,c73]) ).
cnf(c161,plain,
inverse(multiply(X,inverse(inverse(inverse(multiply(inverse(Y),Y)))))) = inverse(multiply(X,multiply(inverse(Z),Z))),
inference(equational,[status(thm)],[c106,c115]) ).
cnf(c168,plain,
multiply(X,inverse(multiply(X,inverse(multiply(inverse(Y),Y))))) = inverse(inverse(multiply(inverse(Z),Z))),
inference(equational,[status(thm)],[c74,c112]) ).
cnf(c174,plain,
inverse(multiply(multiply(inverse(X),X),multiply(Y,Z))) = multiply(inverse(Z),inverse(multiply(Y,multiply(inverse(W),W)))),
inference(equational,[status(thm)],[c63,c74]) ).
cnf(c181,plain,
multiply(inverse(multiply(inverse(X),X)),inverse(multiply(inverse(Y),Y))) = multiply(multiply(inverse(Z),Z),multiply(inverse(W),W)),
inference(equational,[status(thm)],[c40,c73,c74]) ).
cnf(c213,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,multiply(inverse(Y),Y)))) = Y,
inference(equational,[status(thm)],[c8,c74,c156]) ).
cnf(c230,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,multiply(inverse(Z),Z)))) = Y,
inference(equational,[status(thm)],[c61,c213]) ).
cnf(c233,plain,
inverse(multiply(X,multiply(inverse(X),Y))) = inverse(multiply(Z,multiply(inverse(Z),Y))),
inference(equational,[status(thm)],[c23,c230]) ).
cnf(c236,plain,
multiply(X,multiply(inverse(multiply(Y,X)),Z)) = multiply(W,multiply(inverse(multiply(Y,W)),Z)),
inference(equational,[status(thm)],[c12,c230]) ).
cnf(c237,plain,
multiply(inverse(multiply(inverse(inverse(X)),Y)),X) = multiply(inverse(multiply(inverse(inverse(Z)),Y)),Z),
inference(equational,[status(thm)],[c26,c230]) ).
cnf(c239,plain,
inverse(multiply(X,multiply(inverse(X),Y))) = inverse(multiply(Y,inverse(multiply(inverse(Z),Z)))),
inference(equational,[status(thm)],[c85,c233]) ).
cnf(c245,plain,
multiply(multiply(inverse(X),X),Y) = multiply(inverse(multiply(inverse(inverse(Z)),inverse(Y))),Z),
inference(equational,[status(thm)],[c74,c237]) ).
cnf(c254,plain,
multiply(X,inverse(multiply(Y,multiply(inverse(Y),X)))) = inverse(inverse(multiply(inverse(Z),Z))),
inference(equational,[status(thm)],[c168,c239]) ).
cnf(c258,plain,
multiply(X,multiply(inverse(multiply(inverse(Y),Y)),Z)) = multiply(W,multiply(inverse(multiply(inverse(X),W)),Z)),
inference(equational,[status(thm)],[c27,c236]) ).
cnf(c267,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(Z,multiply(inverse(multiply(W,Z)),multiply(W,X))),
inference(equational,[status(thm)],[c27,c236]) ).
cnf(c270,plain,
multiply(inverse(inverse(inverse(multiply(inverse(X),X)))),Y) = multiply(inverse(multiply(inverse(inverse(Z)),inverse(Y))),Z),
inference(equational,[status(thm)],[c75,c237]) ).
cnf(c276,plain,
inverse(inverse(inverse(multiply(inverse(X),X)))) = multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(Z),Z))),
inference(equational,[status(thm)],[c42,c119,c181]) ).
cnf(c277,plain,
inverse(multiply(inverse(X),inverse(inverse(inverse(multiply(inverse(Y),Y)))))) = X,
inference(equational,[status(thm)],[c8,c230,c276]) ).
cnf(c278,plain,
inverse(multiply(inverse(X),multiply(inverse(Y),Y))) = X,
inference(equational,[status(thm)],[c161,c277]) ).
cnf(c279,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = Y,
inference(equational,[status(thm)],[c61,c230,c278]) ).
cnf(c280,plain,
inverse(multiply(inverse(X),Y)) = multiply(inverse(Y),X),
inference(equational,[status(thm)],[c46,c278,c279]) ).
cnf(c281,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference(equational,[status(thm)],[c245,c279]) ).
cnf(c282,plain,
multiply(X,inverse(X)) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c254,c280,c281]) ).
cnf(c283,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c270,c280,c281,c282]) ).
cnf(c285,plain,
multiply(X,multiply(inverse(Y),Y)) = X,
inference(equational,[status(thm)],[c36,c278,c279]) ).
cnf(c288,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c174,c281,c285]) ).
cnf(c289,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c267,c280,c285]) ).
cnf(c298,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c258,c280,c281,c283,c288,c289]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c298]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : GRP423-1 : TPTP v9.0.0. Released v2.6.0.
% 0.02/0.12 % 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
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 08:27:04 EDT 2025
% 0.11/0.32 % CPUTime :
% 83.08/83.19 % SZS status Unsatisfiable
% 83.08/83.19 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------