%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP420-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n009.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 124.96s 125.04s
% Output : CNFRefutation 124.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of clauses : 79 ( 79 unt; 0 nHn; 3 RR)
% Number of literals : 79 ( 78 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 17 ( 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 : 241 ( 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),inverse(multiply(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,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))) = multiply(inverse(multiply(W,inverse(multiply(inverse(Y),inverse(multiply(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,inverse(multiply(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)),inverse(multiply(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,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z))) = inverse(multiply(inverse(multiply(W,inverse(multiply(Y,inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),multiply(W,V))),
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c8,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(inverse(W)),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(X,Z)),multiply(X,Z))))))))),Y) = W,
inference(equational,[status(thm)],[c4]) ).
cnf(c9,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(inverse(W),inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(X,Z)),multiply(X,Z))))))))),Y)) = W,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c10,plain,
multiply(inverse(multiply(X,inverse(multiply(Y,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z)) = inverse(multiply(inverse(multiply(W,inverse(multiply(multiply(inverse(multiply(V,inverse(multiply(inverse(Y),inverse(multiply(U,inverse(multiply(inverse(U),U)))))))),multiply(V,U)),inverse(multiply(U2,inverse(multiply(inverse(U2),U2)))))))),multiply(W,U2))),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c13,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(inverse(Y)),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),inverse(multiply(W,inverse(multiply(multiply(X,Z),inverse(multiply(inverse(multiply(X,Z)),multiply(X,Z))))))))),Y)) = inverse(multiply(inverse(multiply(V,inverse(multiply(W,inverse(multiply(U,inverse(multiply(inverse(U),U)))))))),multiply(V,U))),
inference(equational,[status(thm)],[c2,c4]) ).
cnf(c14,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(Y),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))))),multiply(X,Z)) = inverse(multiply(inverse(multiply(inverse(multiply(W,inverse(multiply(inverse(inverse(V)),inverse(multiply(U,inverse(multiply(inverse(U),U)))))))),inverse(multiply(Y,inverse(multiply(multiply(W,U),inverse(multiply(inverse(multiply(W,U)),multiply(W,U))))))))),V)),
inference(equational,[status(thm)],[c3,c10,c13]) ).
cnf(c18,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))) = multiply(inverse(multiply(W,inverse(multiply(inverse(inverse(inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))),inverse(multiply(V,inverse(multiply(inverse(V),V)))))))),inverse(multiply(inverse(Y),inverse(multiply(multiply(W,V),inverse(multiply(inverse(multiply(W,V)),multiply(W,V)))))))),
inference(equational,[status(thm)],[c1,c6,c9]) ).
cnf(c19,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))) = Y,
inference(equational,[status(thm)],[c9,c18]) ).
cnf(c20,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(multiply(W,Y)),multiply(W,Z)),
inference(equational,[status(thm)],[c4,c19]) ).
cnf(c21,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))) = inverse(multiply(inverse(multiply(W,Y)),multiply(W,Z))),
inference(equational,[status(thm)],[c4,c6,c19]) ).
cnf(c22,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,c19]) ).
cnf(c30,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),inverse(multiply(Z,inverse(multiply(inverse(Z),Z))))) = Y,
inference(equational,[status(thm)],[c8,c18]) ).
cnf(c35,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)))),W)),Y) = multiply(inverse(multiply(V,W)),multiply(V,inverse(multiply(Z,inverse(multiply(inverse(Z),Z)))))),
inference(equational,[status(thm)],[c20,c30]) ).
cnf(c37,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)],[c30,c35]) ).
cnf(c38,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c19,c30,c37]) ).
cnf(c39,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,Z))),
inference(equational,[status(thm)],[c21,c38]) ).
cnf(c40,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(Y),Y)),
inference(equational,[status(thm)],[c30,c35,c39]) ).
cnf(c41,plain,
inverse(inverse(multiply(inverse(X),X))) = inverse(inverse(multiply(inverse(Y),Y))),
inference(equational,[status(thm)],[c22,c38]) ).
cnf(c42,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(W,Y)),multiply(W,X)),
inference(equational,[status(thm)],[c20,c38]) ).
cnf(c44,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(multiply(W,Y)),multiply(W,Z)),
inference(equational,[status(thm)],[c20,c38]) ).
cnf(c46,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)],[c38,c44]) ).
cnf(c47,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = multiply(inverse(multiply(inverse(Z),Z)),Y),
inference(equational,[status(thm)],[c8,c46]) ).
cnf(c48,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)],[c38,c42]) ).
cnf(c49,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(X,multiply(inverse(Z),Z)),
inference(equational,[status(thm)],[c9,c48]) ).
cnf(c51,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z))) = inverse(multiply(inverse(multiply(W,Y)),multiply(W,Z))),
inference(equational,[status(thm)],[c21,c38]) ).
cnf(c52,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)],[c21,c38]) ).
cnf(c53,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),multiply(X,Z)) = multiply(Z,inverse(multiply(inverse(Z),Z))),
inference(equational,[status(thm)],[c9,c14,c38]) ).
cnf(c54,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(Y),Y))) = multiply(inverse(Z),Z),
inference(equational,[status(thm)],[c38,c41]) ).
cnf(c57,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = multiply(inverse(multiply(Z,inverse(multiply(inverse(W),W)))),multiply(Z,X)),
inference(equational,[status(thm)],[c38,c53]) ).
cnf(c58,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = multiply(X,inverse(multiply(inverse(X),X))),
inference(equational,[status(thm)],[c4,c57]) ).
cnf(c59,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = multiply(X,inverse(multiply(inverse(Z),Z))),
inference(equational,[status(thm)],[c40,c58]) ).
cnf(c60,plain,
inverse(multiply(X,inverse(multiply(inverse(Y),Y)))) = inverse(multiply(X,inverse(multiply(inverse(X),X)))),
inference(equational,[status(thm)],[c8,c13,c57]) ).
cnf(c61,plain,
inverse(multiply(X,inverse(multiply(inverse(Y),Y)))) = inverse(multiply(X,inverse(multiply(inverse(Z),Z)))),
inference(equational,[status(thm)],[c58,c60]) ).
cnf(c75,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)],[c20,c49]) ).
cnf(c79,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z))) = inverse(multiply(inverse(multiply(inverse(W),W)),multiply(inverse(Y),Z))),
inference(equational,[status(thm)],[c47,c51]) ).
cnf(c80,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),Y)) = inverse(multiply(inverse(multiply(inverse(Z),Z)),Y)),
inference(equational,[status(thm)],[c8,c79]) ).
cnf(c93,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(Y,inverse(multiply(inverse(Y),Y)))))) = Y,
inference(equational,[status(thm)],[c19,c38]) ).
cnf(c94,plain,
inverse(multiply(inverse(X),X)) = inverse(inverse(multiply(inverse(Y),Y))),
inference(equational,[status(thm)],[c54,c93]) ).
cnf(c95,plain,
multiply(inverse(X),X) = inverse(multiply(inverse(Y),Y)),
inference(equational,[status(thm)],[c30,c94]) ).
cnf(c96,plain,
multiply(inverse(X),X) = inverse(inverse(multiply(inverse(Y),Y))),
inference(equational,[status(thm)],[c38,c94,c95]) ).
cnf(c97,plain,
inverse(inverse(inverse(multiply(inverse(X),X)))) = inverse(multiply(inverse(Y),Y)),
inference(equational,[status(thm)],[c94]) ).
cnf(c98,plain,
inverse(inverse(inverse(multiply(inverse(X),X)))) = inverse(inverse(multiply(inverse(Y),Y))),
inference(equational,[status(thm)],[c41,c94]) ).
cnf(c100,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(X,inverse(multiply(inverse(Z),Z))),
inference(equational,[status(thm)],[c59,c95]) ).
cnf(c103,plain,
multiply(inverse(inverse(multiply(inverse(X),X))),Y) = multiply(inverse(multiply(inverse(Z),Z)),Y),
inference(equational,[status(thm)],[c47,c94]) ).
cnf(c123,plain,
multiply(inverse(inverse(inverse(multiply(inverse(X),X)))),Y) = multiply(inverse(multiply(inverse(Z),Z)),Y),
inference(equational,[status(thm)],[c98,c103]) ).
cnf(c153,plain,
inverse(multiply(X,inverse(inverse(inverse(multiply(inverse(Y),Y)))))) = inverse(multiply(X,inverse(multiply(inverse(Z),Z)))),
inference(equational,[status(thm)],[c61,c97]) ).
cnf(c177,plain,
multiply(inverse(multiply(X,multiply(inverse(Y),Y))),multiply(X,Z)) = multiply(Z,inverse(multiply(inverse(Z),Z))),
inference(equational,[status(thm)],[c9,c14,c95]) ).
cnf(c184,plain,
inverse(multiply(inverse(inverse(inverse(multiply(inverse(X),X)))),Y)) = inverse(multiply(inverse(multiply(inverse(Z),Z)),Y)),
inference(equational,[status(thm)],[c80,c123]) ).
cnf(c196,plain,
multiply(inverse(multiply(X,multiply(inverse(Y),Y))),multiply(X,Z)) = multiply(Z,multiply(inverse(W),W)),
inference(equational,[status(thm)],[c100,c177]) ).
cnf(c218,plain,
multiply(X,inverse(inverse(multiply(inverse(Y),Y)))) = multiply(inverse(multiply(Z,inverse(multiply(inverse(W),W)))),multiply(Z,X)),
inference(equational,[status(thm)],[c57,c94]) ).
cnf(c221,plain,
multiply(X,multiply(inverse(Y),Y)) = multiply(inverse(multiply(Z,inverse(multiply(inverse(W),W)))),multiply(Z,X)),
inference(equational,[status(thm)],[c53,c95]) ).
cnf(c235,plain,
inverse(multiply(multiply(inverse(X),X),multiply(inverse(Y),Z))) = inverse(multiply(inverse(multiply(inverse(Z),Y)),multiply(inverse(W),W))),
inference(equational,[status(thm)],[c52,c95]) ).
cnf(c281,plain,
multiply(X,inverse(inverse(multiply(inverse(Y),Y)))) = multiply(inverse(multiply(Z,multiply(inverse(W),W))),multiply(Z,X)),
inference(equational,[status(thm)],[c44,c95,c218]) ).
cnf(c387,plain,
inverse(multiply(multiply(inverse(X),X),inverse(multiply(Y,inverse(multiply(inverse(Y),Y)))))) = Y,
inference(equational,[status(thm)],[c93,c96]) ).
cnf(c388,plain,
inverse(multiply(multiply(inverse(X),X),inverse(multiply(Y,multiply(inverse(Z),Z))))) = Y,
inference(equational,[status(thm)],[c95,c387]) ).
cnf(c389,plain,
inverse(multiply(inverse(X),multiply(inverse(Y),Y))) = X,
inference(equational,[status(thm)],[c177,c387,c388]) ).
cnf(c390,plain,
multiply(X,multiply(inverse(X),Y)) = multiply(Y,multiply(inverse(Z),Z)),
inference(equational,[status(thm)],[c196,c389]) ).
cnf(c391,plain,
inverse(multiply(multiply(inverse(X),X),Y)) = inverse(Y),
inference(equational,[status(thm)],[c388,c389]) ).
cnf(c392,plain,
inverse(multiply(inverse(X),Y)) = multiply(inverse(Y),X),
inference(equational,[status(thm)],[c235,c389,c391]) ).
cnf(c393,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference(equational,[status(thm)],[c8,c391]) ).
cnf(c394,plain,
multiply(X,multiply(inverse(Y),Y)) = X,
inference(equational,[status(thm)],[c281,c392,c393]) ).
cnf(c395,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c388,c393,c394]) ).
cnf(c396,plain,
multiply(X,inverse(X)) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c390,c393,c394]) ).
cnf(c398,plain,
multiply(X,multiply(Y,inverse(Y))) = X,
inference(equational,[status(thm)],[c221,c392,c393,c396]) ).
cnf(c399,plain,
multiply(multiply(X,inverse(X)),Y) = Y,
inference(equational,[status(thm)],[c153,c389,c392,c396]) ).
cnf(c400,plain,
inverse(multiply(X,inverse(X))) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c184,c388,c392,c396]) ).
cnf(c402,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c1,c392,c393,c395,c398,c399,c400]) ).
cnf(c403,plain,
multiply(multiply(X,Y),inverse(Y)) = X,
inference(equational,[status(thm)],[c30,c392,c394,c395,c399,c400]) ).
cnf(c405,plain,
multiply(inverse(multiply(X,Y)),X) = inverse(Y),
inference(equational,[status(thm)],[c75,c394,c395,c399,c400]) ).
cnf(c406,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c53,c392,c394,c405]) ).
cnf(c408,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(equational,[status(thm)],[c402,c403]) ).
cnf(c412,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c51,c392,c393,c395,c406,c408]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c412]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP420-1 : TPTP v9.0.0. Released v2.6.0.
% 0.00/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n009.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 :
% 124.96/125.04 % SZS status Unsatisfiable
% 124.96/125.04 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------