%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP440-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n003.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 6.69s 6.90s
% Output : CNFRefutation 6.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of clauses : 52 ( 52 unt; 0 nHn; 3 RR)
% Number of literals : 52 ( 51 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 170 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c1,axiom,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),Z),inverse(multiply(W,multiply(X,Z))))))) = W,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),Z),inverse(multiply(W,multiply(V,Z))))),W)))) = V,
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),multiply(multiply(inverse(Z),W),inverse(multiply(V,multiply(U,W))))),V)),U)))) = Z,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
inverse(multiply(X,multiply(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),W),inverse(multiply(V,multiply(Y,W)))))),multiply(multiply(V,U),inverse(multiply(U2,multiply(X,U))))))) = U2,
inference(equational,[status(thm)],[c1]) ).
cnf(c5,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),multiply(multiply(Z,W),inverse(multiply(V,multiply(U,W))))),V)),U)))) = multiply(U2,multiply(U3,multiply(multiply(inverse(U3),U4),inverse(multiply(Z,multiply(U2,U4)))))),
inference(equational,[status(thm)],[c2,c4]) ).
cnf(c6,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),Z),inverse(multiply(inverse(W),multiply(X,Z)))))) = W,
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c11,plain,
inverse(inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),multiply(multiply(Z,W),inverse(multiply(V,multiply(U,W))))),V)),U))))) = Z,
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c13,plain,
inverse(multiply(X,multiply(Y,multiply(Z,inverse(multiply(W,multiply(X,multiply(V,multiply(multiply(inverse(V),U),inverse(multiply(inverse(Z),multiply(inverse(Y),U)))))))))))) = W,
inference(equational,[status(thm)],[c1,c6]) ).
cnf(c14,plain,
inverse(multiply(inverse(X),multiply(X,multiply(Y,inverse(multiply(Z,Y)))))) = Z,
inference(equational,[status(thm)],[c6,c13]) ).
cnf(c15,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(Z,inverse(multiply(W,Z)))),W))) = X,
inference(equational,[status(thm)],[c6,c14]) ).
cnf(c16,plain,
multiply(X,multiply(Y,multiply(inverse(Y),inverse(multiply(inverse(Z),X))))) = Z,
inference(equational,[status(thm)],[c6,c15]) ).
cnf(c17,plain,
inverse(multiply(X,multiply(Y,multiply(inverse(Y),inverse(multiply(Z,X)))))) = Z,
inference(equational,[status(thm)],[c1,c15]) ).
cnf(c19,plain,
multiply(X,multiply(Y,multiply(inverse(Y),inverse(multiply(Z,X))))) = multiply(inverse(W),multiply(W,multiply(V,inverse(multiply(Z,V))))),
inference(equational,[status(thm)],[c14,c16]) ).
cnf(c20,plain,
multiply(inverse(X),multiply(X,multiply(Y,inverse(multiply(inverse(Z),Y))))) = Z,
inference(equational,[status(thm)],[c16,c19]) ).
cnf(c22,plain,
multiply(multiply(X,multiply(Y,inverse(multiply(Z,Y)))),multiply(W,multiply(inverse(W),Z))) = X,
inference(equational,[status(thm)],[c14,c16]) ).
cnf(c25,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),Z),inverse(multiply(W,multiply(X,Z)))))) = multiply(inverse(V),multiply(V,multiply(U,inverse(multiply(W,U))))),
inference(equational,[status(thm)],[c6,c14]) ).
cnf(c26,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(inverse(X),inverse(multiply(Z,W)))),Z)))) = W,
inference(equational,[status(thm)],[c2,c15]) ).
cnf(c27,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(inverse(X),Z)),W)))) = multiply(V,multiply(inverse(V),inverse(multiply(Z,W)))),
inference(equational,[status(thm)],[c17,c26]) ).
cnf(c28,plain,
multiply(X,multiply(inverse(X),inverse(multiply(inverse(multiply(Y,Z)),Y)))) = Z,
inference(equational,[status(thm)],[c26,c27]) ).
cnf(c29,plain,
multiply(X,multiply(inverse(X),Y)) = multiply(Z,multiply(inverse(Z),Y)),
inference(equational,[status(thm)],[c14,c22,c28]) ).
cnf(c30,plain,
multiply(X,inverse(X)) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c15,c29]) ).
cnf(c31,plain,
multiply(X,multiply(Y,inverse(Y))) = multiply(Z,multiply(inverse(Z),inverse(inverse(X)))),
inference(equational,[status(thm)],[c29,c30]) ).
cnf(c33,plain,
multiply(X,multiply(inverse(X),inverse(multiply(Y,inverse(Z))))) = multiply(Z,multiply(W,inverse(multiply(Y,W)))),
inference(equational,[status(thm)],[c1,c25,c28]) ).
cnf(c34,plain,
multiply(X,multiply(Y,multiply(Z,inverse(multiply(inverse(inverse(Y)),Z))))) = X,
inference(equational,[status(thm)],[c15,c28]) ).
cnf(c35,plain,
multiply(X,multiply(inverse(X),inverse(multiply(inverse(Y),Z)))) = multiply(inverse(Z),inverse(multiply(inverse(multiply(W,Y)),W))),
inference(equational,[status(thm)],[c28]) ).
cnf(c38,plain,
multiply(X,multiply(Y,inverse(multiply(inverse(multiply(inverse(X),Z)),Y)))) = Z,
inference(equational,[status(thm)],[c28,c33]) ).
cnf(c39,plain,
multiply(X,multiply(Y,inverse(multiply(Z,Y)))) = multiply(X,multiply(W,inverse(multiply(Z,W)))),
inference(equational,[status(thm)],[c1,c25,c38]) ).
cnf(c40,plain,
multiply(X,inverse(multiply(Y,X))) = multiply(Z,inverse(multiply(Y,Z))),
inference(equational,[status(thm)],[c28,c39]) ).
cnf(c42,plain,
multiply(inverse(X),inverse(multiply(inverse(multiply(Y,multiply(X,Z))),Y))) = Z,
inference(equational,[status(thm)],[c16,c35]) ).
cnf(c43,plain,
multiply(inverse(X),multiply(X,Y)) = multiply(inverse(Z),multiply(Z,Y)),
inference(equational,[status(thm)],[c16,c19,c42]) ).
cnf(c44,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c34,c43]) ).
cnf(c46,plain,
inverse(multiply(inverse(X),multiply(X,Y))) = inverse(multiply(inverse(Z),multiply(Z,Y))),
inference(equational,[status(thm)],[c14,c42]) ).
cnf(c47,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(Y),Y)),
inference(equational,[status(thm)],[c34,c46]) ).
cnf(c49,plain,
multiply(inverse(X),multiply(Y,inverse(Y))) = multiply(inverse(Z),multiply(Z,inverse(X))),
inference(equational,[status(thm)],[c30,c43]) ).
cnf(c50,plain,
multiply(inverse(X),multiply(X,Y)) = multiply(Y,multiply(Z,inverse(Z))),
inference(equational,[status(thm)],[c11,c49]) ).
cnf(c51,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = multiply(Z,inverse(multiply(inverse(X),Z))),
inference(equational,[status(thm)],[c40,c47]) ).
cnf(c57,plain,
multiply(inverse(inverse(X)),multiply(inverse(Y),Y)) = multiply(X,multiply(Z,inverse(Z))),
inference(equational,[status(thm)],[c31,c44]) ).
cnf(c65,plain,
multiply(multiply(X,Y),inverse(multiply(Z,multiply(W,Y)))) = multiply(X,inverse(multiply(Z,W))),
inference(equational,[status(thm)],[c1,c4,c42]) ).
cnf(c72,plain,
multiply(X,multiply(multiply(inverse(X),Y),inverse(multiply(inverse(Y),Y)))) = Y,
inference(equational,[status(thm)],[c16,c33,c35,c51]) ).
cnf(c73,plain,
multiply(X,multiply(Y,inverse(Y))) = X,
inference(equational,[status(thm)],[c30,c72]) ).
cnf(c74,plain,
multiply(inverse(X),X) = multiply(Y,inverse(Y)),
inference(equational,[status(thm)],[c50,c73]) ).
cnf(c75,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c57,c73,c74]) ).
cnf(c76,plain,
inverse(multiply(X,inverse(X))) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c44,c73]) ).
cnf(c78,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c16,c25,c65,c73,c75,c76]) ).
cnf(c81,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference(equational,[status(thm)],[c72,c73,c75,c76]) ).
cnf(c88,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(equational,[status(thm)],[c34,c75,c78]) ).
cnf(c91,plain,
multiply(multiply(X,inverse(Y)),inverse(Z)) = multiply(X,inverse(multiply(Z,Y))),
inference(equational,[status(thm)],[c65,c73]) ).
cnf(c92,plain,
multiply(multiply(X,inverse(X)),Y) = Y,
inference(equational,[status(thm)],[c20,c75,c78,c91]) ).
cnf(c94,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference(equational,[status(thm)],[c4,c65,c78,c81,c88,c92]) ).
cnf(g1,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(equational,[status(thm)],[c94]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP440-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n003.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 08:28:04 EDT 2025
% 0.11/0.32 % CPUTime :
% 6.69/6.90 % SZS status Unsatisfiable
% 6.69/6.90 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------