%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP435-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n007.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 06:44:03 AM UTC 2025
% Result : Unsatisfiable 83.13s 83.23s
% Output : CNFRefutation 83.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 2
% Syntax : Number of clauses : 89 ( 89 unt; 0 nHn; 3 RR)
% Number of literals : 89 ( 88 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 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 : 252 ( 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(multiply(multiply(inverse(multiply(multiply(X,Y),Z)),X),Y),multiply(W,inverse(W)))) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
inverse(multiply(multiply(multiply(X,multiply(inverse(multiply(multiply(Y,Z),X)),Y)),Z),multiply(W,inverse(W)))) = multiply(V,inverse(V)),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
multiply(multiply(multiply(multiply(inverse(multiply(multiply(X,Y),Z)),X),Y),multiply(W,inverse(W))),Z) = inverse(multiply(multiply(multiply(V,multiply(inverse(multiply(multiply(U,U2),V)),U)),U2),multiply(U3,inverse(U3)))),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
multiply(multiply(multiply(multiply(inverse(multiply(multiply(X,Y),Z)),X),Y),multiply(W,inverse(W))),Z) = multiply(V,inverse(V)),
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c6,plain,
inverse(multiply(multiply(multiply(multiply(X,inverse(X)),multiply(Y,multiply(inverse(multiply(multiply(Z,W),Y)),Z))),W),multiply(V,inverse(V)))) = multiply(U,inverse(U)),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c7,plain,
multiply(X,inverse(X)) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c1,c2,c6]) ).
cnf(c8,plain,
inverse(multiply(multiply(multiply(inverse(multiply(X,inverse(X))),Y),Z),multiply(W,inverse(W)))) = inverse(multiply(Y,Z)),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c9,plain,
inverse(multiply(multiply(X,inverse(X)),multiply(Y,inverse(Y)))) = inverse(multiply(Z,inverse(multiply(inverse(multiply(W,inverse(W))),Z)))),
inference(equational,[status(thm)],[c7,c8]) ).
cnf(c10,plain,
inverse(multiply(multiply(multiply(X,inverse(X)),Y),multiply(Z,inverse(Z)))) = inverse(multiply(inverse(inverse(multiply(W,inverse(W)))),Y)),
inference(equational,[status(thm)],[c7,c8]) ).
cnf(c11,plain,
inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),Y)) = inverse(multiply(inverse(inverse(multiply(Z,inverse(Z)))),Y)),
inference(equational,[status(thm)],[c8,c10]) ).
cnf(c13,plain,
inverse(multiply(multiply(inverse(multiply(multiply(X,Y),inverse(multiply(Z,inverse(Z))))),X),Y)) = multiply(W,inverse(W)),
inference(equational,[status(thm)],[c2,c8]) ).
cnf(c14,plain,
inverse(multiply(multiply(inverse(multiply(X,inverse(X))),Y),inverse(Y))) = multiply(Z,inverse(Z)),
inference(equational,[status(thm)],[c7,c13]) ).
cnf(c16,plain,
inverse(multiply(multiply(X,inverse(X)),inverse(inverse(inverse(multiply(Y,inverse(Y))))))) = multiply(Z,inverse(Z)),
inference(equational,[status(thm)],[c7,c14]) ).
cnf(c17,plain,
inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),inverse(multiply(Y,inverse(Y))))) = inverse(multiply(multiply(Z,inverse(Z)),multiply(W,inverse(W)))),
inference(equational,[status(thm)],[c7,c9]) ).
cnf(c18,plain,
inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),inverse(multiply(Y,inverse(Y))))) = inverse(multiply(Z,inverse(multiply(inverse(multiply(W,inverse(W))),Z)))),
inference(equational,[status(thm)],[c9,c10]) ).
cnf(c19,plain,
multiply(multiply(multiply(inverse(multiply(X,inverse(X))),Y),inverse(Y)),multiply(Z,inverse(Z))) = multiply(W,inverse(W)),
inference(equational,[status(thm)],[c7,c14]) ).
cnf(c20,plain,
inverse(multiply(X,inverse(X))) = inverse(multiply(Y,inverse(Y))),
inference(equational,[status(thm)],[c8,c19]) ).
cnf(c21,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(Y,inverse(Y)))) = multiply(Z,inverse(Z)),
inference(equational,[status(thm)],[c4,c19]) ).
cnf(c22,plain,
inverse(multiply(multiply(X,inverse(X)),inverse(multiply(Y,inverse(Y))))) = inverse(multiply(Z,inverse(Z))),
inference(equational,[status(thm)],[c20,c21]) ).
cnf(c23,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(Y,inverse(Y)))) = multiply(multiply(Z,inverse(Z)),inverse(multiply(W,inverse(W)))),
inference(equational,[status(thm)],[c20,c21]) ).
cnf(c24,plain,
inverse(inverse(multiply(multiply(inverse(multiply(X,inverse(X))),Y),inverse(Y)))) = inverse(multiply(Z,inverse(Z))),
inference(equational,[status(thm)],[c14,c20]) ).
cnf(c27,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X,inverse(X)),Y)),Z),inverse(Z)),multiply(W,inverse(W)))) = Y,
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c28,plain,
multiply(X,inverse(X)) = inverse(multiply(inverse(multiply(Y,inverse(Y))),multiply(Z,inverse(Z)))),
inference(equational,[status(thm)],[c9,c27]) ).
cnf(c38,plain,
inverse(multiply(multiply(multiply(multiply(X,inverse(X)),Y),inverse(Y)),multiply(Z,inverse(Z)))) = inverse(inverse(inverse(multiply(W,inverse(W))))),
inference(equational,[status(thm)],[c14,c27]) ).
cnf(c39,plain,
inverse(inverse(inverse(multiply(X,inverse(X))))) = inverse(inverse(inverse(multiply(Y,inverse(Y))))),
inference(equational,[status(thm)],[c16,c27,c38]) ).
cnf(c41,plain,
multiply(inverse(inverse(multiply(X,inverse(X)))),inverse(inverse(inverse(multiply(Y,inverse(Y)))))) = multiply(Z,inverse(Z)),
inference(equational,[status(thm)],[c7,c39]) ).
cnf(c42,plain,
inverse(inverse(inverse(multiply(X,inverse(X))))) = inverse(multiply(inverse(inverse(multiply(Y,inverse(Y)))),inverse(inverse(multiply(Z,inverse(Z)))))),
inference(equational,[status(thm)],[c10,c38]) ).
cnf(c43,plain,
inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),inverse(inverse(inverse(multiply(multiply(Y,inverse(Y)),Z)))))) = Z,
inference(equational,[status(thm)],[c10,c27]) ).
cnf(c46,plain,
inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),inverse(multiply(Y,inverse(Y))))) = multiply(Z,inverse(Z)),
inference(equational,[status(thm)],[c10,c13,c14]) ).
cnf(c47,plain,
multiply(X,inverse(X)) = inverse(multiply(multiply(Y,inverse(Y)),multiply(Z,inverse(Z)))),
inference(equational,[status(thm)],[c17,c46]) ).
cnf(c48,plain,
multiply(X,inverse(X)) = inverse(inverse(inverse(multiply(Y,inverse(Y))))),
inference(equational,[status(thm)],[c42,c43,c47]) ).
cnf(c49,plain,
inverse(inverse(inverse(inverse(multiply(X,inverse(X)))))) = inverse(multiply(Y,inverse(Y))),
inference(equational,[status(thm)],[c20,c48]) ).
cnf(c50,plain,
multiply(X,inverse(X)) = inverse(multiply(Y,inverse(multiply(inverse(multiply(Z,inverse(Z))),Y)))),
inference(equational,[status(thm)],[c18,c46]) ).
cnf(c51,plain,
inverse(inverse(inverse(inverse(inverse(inverse(multiply(X,inverse(X)))))))) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c48]) ).
cnf(c52,plain,
multiply(multiply(X,inverse(X)),inverse(multiply(Y,inverse(Y)))) = inverse(inverse(inverse(multiply(Z,inverse(Z))))),
inference(equational,[status(thm)],[c20,c48]) ).
cnf(c55,plain,
multiply(inverse(inverse(multiply(X,inverse(X)))),multiply(Y,inverse(Y))) = multiply(Z,inverse(Z)),
inference(equational,[status(thm)],[c41,c48]) ).
cnf(c58,plain,
multiply(inverse(inverse(multiply(X,inverse(X)))),multiply(Y,inverse(Y))) = inverse(inverse(inverse(multiply(Z,inverse(Z))))),
inference(equational,[status(thm)],[c48]) ).
cnf(c62,plain,
inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(X,inverse(X))))))))) = inverse(multiply(Y,inverse(Y))),
inference(equational,[status(thm)],[c48,c49]) ).
cnf(c65,plain,
inverse(inverse(inverse(inverse(inverse(inverse(multiply(X,inverse(X)))))))) = multiply(multiply(Y,inverse(Y)),inverse(multiply(Z,inverse(Z)))),
inference(equational,[status(thm)],[c23,c51]) ).
cnf(c74,plain,
multiply(inverse(inverse(multiply(X,inverse(X)))),multiply(Y,inverse(Y))) = inverse(multiply(multiply(inverse(multiply(Z,inverse(Z))),W),inverse(W))),
inference(equational,[status(thm)],[c14,c48]) ).
cnf(c78,plain,
inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(X,inverse(X))))))))))) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c23,c48,c65]) ).
cnf(c84,plain,
inverse(inverse(inverse(inverse(multiply(X,inverse(X)))))) = inverse(inverse(multiply(multiply(inverse(multiply(Y,inverse(Y))),Z),inverse(Z)))),
inference(equational,[status(thm)],[c24,c48]) ).
cnf(c88,plain,
inverse(inverse(inverse(inverse(inverse(inverse(multiply(X,inverse(X)))))))) = inverse(multiply(inverse(multiply(Y,inverse(Y))),multiply(Z,inverse(Z)))),
inference(equational,[status(thm)],[c28,c51]) ).
cnf(c92,plain,
inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X,inverse(X))))))),Y)) = inverse(multiply(inverse(inverse(multiply(Z,inverse(Z)))),Y)),
inference(equational,[status(thm)],[c11,c48]) ).
cnf(c94,plain,
inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),multiply(Y,inverse(Y)))) = inverse(inverse(inverse(inverse(multiply(Z,inverse(Z)))))),
inference(equational,[status(thm)],[c74,c84]) ).
cnf(c105,plain,
inverse(multiply(multiply(inverse(inverse(inverse(inverse(multiply(X,inverse(X)))))),Y),inverse(Y))) = multiply(Z,inverse(Z)),
inference(equational,[status(thm)],[c13,c48]) ).
cnf(c143,plain,
inverse(multiply(multiply(multiply(multiply(X,inverse(X)),Y),Z),multiply(W,inverse(W)))) = inverse(multiply(inverse(multiply(V,inverse(V))),multiply(Y,Z))),
inference(equational,[status(thm)],[c1,c50]) ).
cnf(c144,plain,
multiply(inverse(inverse(inverse(inverse(inverse(multiply(X,inverse(X))))))),multiply(Y,inverse(Y))) = multiply(Z,inverse(Z)),
inference(equational,[status(thm)],[c48,c55]) ).
cnf(c155,plain,
multiply(inverse(inverse(multiply(X,inverse(X)))),inverse(inverse(inverse(multiply(Y,inverse(Y)))))) = inverse(inverse(inverse(multiply(Z,inverse(Z))))),
inference(equational,[status(thm)],[c39,c48]) ).
cnf(c157,plain,
inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(multiply(X,inverse(X)))))))))))) = inverse(multiply(Y,inverse(Y))),
inference(equational,[status(thm)],[c22,c49,c65]) ).
cnf(c168,plain,
inverse(multiply(inverse(multiply(X,inverse(X))),multiply(inverse(multiply(Y,inverse(Y))),Z))) = inverse(multiply(inverse(inverse(multiply(W,inverse(W)))),Z)),
inference(equational,[status(thm)],[c10,c143]) ).
cnf(c204,plain,
inverse(multiply(multiply(inverse(inverse(inverse(inverse(multiply(X,inverse(X)))))),Y),inverse(Y))) = inverse(inverse(inverse(multiply(Z,inverse(Z))))),
inference(equational,[status(thm)],[c52,c105]) ).
cnf(c209,plain,
inverse(multiply(multiply(X,inverse(multiply(inverse(multiply(Y,inverse(Y))),X))),multiply(Z,inverse(Z)))) = inverse(multiply(W,inverse(W))),
inference(equational,[status(thm)],[c20,c50]) ).
cnf(c210,plain,
inverse(multiply(X,inverse(multiply(inverse(inverse(multiply(Y,inverse(Y)))),X)))) = inverse(multiply(Z,inverse(Z))),
inference(equational,[status(thm)],[c8,c168,c209]) ).
cnf(c211,plain,
inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),multiply(Y,Z))) = inverse(multiply(Y,Z)),
inference(equational,[status(thm)],[c1,c8,c210]) ).
cnf(c212,plain,
inverse(inverse(inverse(inverse(inverse(inverse(multiply(X,inverse(X)))))))) = inverse(multiply(Y,inverse(Y))),
inference(equational,[status(thm)],[c46,c88,c210]) ).
cnf(c213,plain,
inverse(multiply(X,inverse(X))) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c51,c212]) ).
cnf(c215,plain,
inverse(inverse(multiply(X,inverse(X)))) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c62,c212,c213]) ).
cnf(c216,plain,
inverse(inverse(inverse(multiply(X,inverse(X))))) = inverse(multiply(Y,inverse(Y))),
inference(equational,[status(thm)],[c94,c211,c212]) ).
cnf(c217,plain,
inverse(inverse(inverse(inverse(multiply(X,inverse(X)))))) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c78,c212]) ).
cnf(c218,plain,
inverse(inverse(inverse(inverse(inverse(multiply(X,inverse(X))))))) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c157,c212,c213]) ).
cnf(c220,plain,
inverse(multiply(multiply(X,inverse(X)),multiply(Y,Z))) = inverse(multiply(Y,Z)),
inference(equational,[status(thm)],[c211,c215]) ).
cnf(c226,plain,
inverse(multiply(multiply(X,inverse(X)),Y)) = inverse(multiply(multiply(Z,inverse(Z)),Y)),
inference(equational,[status(thm)],[c92,c213,c218]) ).
cnf(c227,plain,
inverse(multiply(inverse(multiply(X,inverse(X))),Y)) = inverse(multiply(multiply(Z,inverse(Z)),Y)),
inference(equational,[status(thm)],[c47,c220,c226]) ).
cnf(c228,plain,
multiply(inverse(multiply(X,inverse(X))),multiply(Y,inverse(Y))) = multiply(Z,inverse(Z)),
inference(equational,[status(thm)],[c144,c217]) ).
cnf(c238,plain,
inverse(multiply(multiply(X,inverse(X)),Y)) = inverse(multiply(inverse(inverse(multiply(Z,inverse(Z)))),Y)),
inference(equational,[status(thm)],[c8,c10,c228]) ).
cnf(c242,plain,
inverse(multiply(multiply(multiply(X,inverse(X)),Y),inverse(Y))) = inverse(multiply(Z,inverse(Z))),
inference(equational,[status(thm)],[c204,c216,c217]) ).
cnf(c243,plain,
inverse(multiply(multiply(X,inverse(X)),Y)) = inverse(Y),
inference(equational,[status(thm)],[c1,c8,c242]) ).
cnf(c245,plain,
inverse(multiply(inverse(inverse(multiply(X,inverse(X)))),Y)) = inverse(Y),
inference(equational,[status(thm)],[c227,c243]) ).
cnf(c246,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference(equational,[status(thm)],[c43,c243,c245]) ).
cnf(c247,plain,
multiply(multiply(X,inverse(X)),Y) = Y,
inference(equational,[status(thm)],[c238,c245,c246]) ).
cnf(c248,plain,
multiply(inverse(inverse(inverse(X))),X) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c7,c246]) ).
cnf(c252,plain,
inverse(multiply(X,multiply(Y,inverse(Y)))) = inverse(X),
inference(equational,[status(thm)],[c10,c245,c247]) ).
cnf(c269,plain,
multiply(inverse(inverse(multiply(X,inverse(X)))),Y) = Y,
inference(equational,[status(thm)],[c245,c246]) ).
cnf(c272,plain,
inverse(inverse(inverse(multiply(X,inverse(X))))) = multiply(inverse(inverse(inverse(Y))),Y),
inference(equational,[status(thm)],[c248,c269]) ).
cnf(c274,plain,
inverse(multiply(multiply(inverse(inverse(inverse(X))),X),Y)) = inverse(Y),
inference(equational,[status(thm)],[c155,c243,c272]) ).
cnf(c279,plain,
inverse(multiply(multiply(inverse(X),inverse(inverse(inverse(Y)))),Y)) = X,
inference(equational,[status(thm)],[c1,c252,c274]) ).
cnf(c280,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c58,c252,c269,c279]) ).
cnf(c283,plain,
multiply(X,multiply(Y,inverse(Y))) = X,
inference(equational,[status(thm)],[c252,c279]) ).
cnf(c293,plain,
inverse(multiply(inverse(multiply(X,Y)),X)) = Y,
inference(equational,[status(thm)],[c1,c283]) ).
cnf(c294,plain,
multiply(inverse(multiply(X,Y)),X) = inverse(Y),
inference(equational,[status(thm)],[c280,c293]) ).
cnf(c295,plain,
inverse(multiply(inverse(X),Y)) = multiply(inverse(Y),X),
inference(equational,[status(thm)],[c279,c280,c294]) ).
cnf(c299,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(equational,[status(thm)],[c280,c294]) ).
cnf(c300,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c246,c280,c295]) ).
cnf(c304,plain,
inverse(multiply(multiply(X,Y),Z)) = inverse(multiply(X,multiply(Y,Z))),
inference(equational,[status(thm)],[c1,c280,c283,c299]) ).
cnf(c305,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c279,c280,c294,c300,c304]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c305]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP435-1 : TPTP v9.0.0. Released v2.6.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % 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 08:27:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 83.13/83.23 % SZS status Unsatisfiable
% 83.13/83.23 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------