%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP505-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n010.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 06:44:12 AM UTC 2025
% Result : Unsatisfiable 268.19s 268.29s
% Output : CNFRefutation 268.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 3 RR)
% Number of literals : 36 ( 35 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 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 : 186 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c1,axiom,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,W)),multiply(Z,inverse(multiply(multiply(V,inverse(U)),inverse(W))))))),U) = V,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,W)),multiply(Z,inverse(multiply(V,inverse(W))))))),U) = inverse(multiply(inverse(multiply(inverse(multiply(U2,U3)),multiply(U3,U2))),multiply(inverse(multiply(U4,U5)),multiply(U4,inverse(multiply(multiply(V,inverse(inverse(U))),inverse(U5))))))),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,W)),multiply(Z,inverse(multiply(V,inverse(W))))))),U),inverse(U)) = V,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,inverse(W))),multiply(Z,inverse(V))))),W) = inverse(multiply(inverse(multiply(inverse(multiply(U,U2)),multiply(U2,U))),multiply(inverse(multiply(U3,U4)),multiply(U3,inverse(multiply(V,inverse(U4))))))),
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c6,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,inverse(W))),multiply(Z,inverse(multiply(V,inverse(U))))))),W),U) = V,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c7,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,inverse(W))),multiply(Z,inverse(V))))),W),U),inverse(U)) = V,
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c8,plain,
multiply(multiply(X,Y),inverse(Y)) = multiply(multiply(X,inverse(Z)),inverse(inverse(Z))),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c9,plain,
multiply(multiply(multiply(X,Y),inverse(Y)),inverse(inverse(inverse(Z)))) = multiply(multiply(multiply(X,inverse(Z)),W),inverse(W)),
inference(equational,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(multiply(multiply(X,inverse(Y)),Z),inverse(Z)) = multiply(multiply(multiply(X,inverse(Y)),W),inverse(W)),
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c11,plain,
multiply(multiply(X,Y),inverse(Y)) = multiply(multiply(X,Z),inverse(Z)),
inference(equational,[status(thm)],[c1,c10]) ).
cnf(c89,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,W)),multiply(Z,inverse(multiply(multiply(multiply(V,inverse(U)),inverse(inverse(U))),inverse(W))))))) = V,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c110,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,W)),multiply(Z,inverse(multiply(multiply(multiply(V,U),inverse(U)),inverse(W))))))) = V,
inference(equational,[status(thm)],[c89]) ).
cnf(c111,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,inverse(W))),multiply(Z,inverse(V))))) = inverse(multiply(inverse(multiply(inverse(multiply(U,U2)),multiply(U2,U))),multiply(inverse(multiply(U3,inverse(W))),multiply(U3,inverse(V))))),
inference(equational,[status(thm)],[c7,c110]) ).
cnf(c112,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,inverse(W))),multiply(Z,inverse(V)))) = multiply(inverse(multiply(inverse(multiply(U,U2)),multiply(U2,U))),multiply(inverse(multiply(U3,inverse(W))),multiply(U3,inverse(V)))),
inference(equational,[status(thm)],[c7,c111]) ).
cnf(c113,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,W)),multiply(Z,inverse(V)))) = multiply(inverse(multiply(inverse(multiply(U,U2)),multiply(U2,U))),multiply(inverse(multiply(U3,W)),multiply(U3,inverse(V)))),
inference(equational,[status(thm)],[c110,c112]) ).
cnf(c114,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,W)),multiply(Z,V))) = multiply(inverse(multiply(inverse(multiply(U,U2)),multiply(U2,U))),multiply(inverse(multiply(U3,W)),multiply(U3,V))),
inference(equational,[status(thm)],[c110,c113]) ).
cnf(c120,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,inverse(W))),multiply(Z,inverse(multiply(multiply(V,U),inverse(U))))))),W) = V,
inference(equational,[status(thm)],[c4,c110]) ).
cnf(c139,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(Z,inverse(W))),multiply(Z,inverse(multiply(multiply(multiply(V,W),U),inverse(U))))))) = V,
inference(equational,[status(thm)],[c8,c110]) ).
cnf(c173,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(multiply(multiply(Z,W),inverse(W))),multiply(multiply(Z,V),U))) = multiply(inverse(multiply(inverse(multiply(U2,U3)),multiply(U3,U2))),multiply(inverse(multiply(U4,inverse(V))),multiply(U4,U))),
inference(equational,[status(thm)],[c11,c114]) ).
cnf(c174,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(Z),Z)) = multiply(inverse(multiply(inverse(multiply(W,V)),multiply(V,W))),multiply(inverse(multiply(U,inverse(U2))),multiply(U,inverse(U2)))),
inference(equational,[status(thm)],[c3,c173]) ).
cnf(c175,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(Z),Z)) = multiply(inverse(multiply(inverse(multiply(W,V)),multiply(V,W))),multiply(inverse(U),U)),
inference(equational,[status(thm)],[c120,c174]) ).
cnf(c243,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(Z),Z))),multiply(multiply(W,V),inverse(V))) = W,
inference(equational,[status(thm)],[c120,c174]) ).
cnf(c252,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(Z),Z))),multiply(W,inverse(V))),V) = W,
inference(equational,[status(thm)],[c6,c174]) ).
cnf(c369,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X)))),multiply(inverse(Z),Z))),multiply(multiply(W,V),inverse(V))) = W,
inference(equational,[status(thm)],[c243]) ).
cnf(c379,plain,
multiply(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X)))),multiply(inverse(Z),Z))),multiply(W,inverse(V))),V) = W,
inference(equational,[status(thm)],[c243,c252]) ).
cnf(c398,plain,
multiply(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))),multiply(inverse(Z),Z)),inverse(multiply(inverse(W),W))) = multiply(multiply(inverse(multiply(inverse(multiply(V,U)),multiply(U,V))),U2),inverse(U2)),
inference(equational,[status(thm)],[c11,c175]) ).
cnf(c399,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(Y,X))) = inverse(multiply(inverse(multiply(Z,W)),multiply(W,Z))),
inference(equational,[status(thm)],[c369,c398]) ).
cnf(c400,plain,
multiply(inverse(multiply(X,Y)),multiply(Y,X)) = multiply(inverse(multiply(Z,W)),multiply(W,Z)),
inference(equational,[status(thm)],[c7,c399]) ).
cnf(c407,plain,
multiply(multiply(inverse(multiply(X,Y)),multiply(Y,X)),inverse(multiply(Z,W))) = multiply(multiply(inverse(multiply(W,Z)),V),inverse(V)),
inference(equational,[status(thm)],[c11,c400]) ).
cnf(c409,plain,
multiply(multiply(inverse(multiply(multiply(X,Y),inverse(multiply(Y,X)))),Z),inverse(Z)) = multiply(inverse(W),W),
inference(equational,[status(thm)],[c379,c407]) ).
cnf(c410,plain,
multiply(inverse(multiply(multiply(X,Y),inverse(multiply(Y,X)))),Z) = inverse(inverse(Z)),
inference(equational,[status(thm)],[c369,c379,c409]) ).
cnf(c411,plain,
multiply(inverse(inverse(X)),inverse(X)) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c409,c410]) ).
cnf(c412,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c139,c411]) ).
cnf(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c412]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP505-1 : TPTP v9.0.0. Released v2.6.0.
% 0.00/0.11 % Command : run_Leo-III %s %d THM
% 0.10/0.31 % Computer : n010.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon Jul 14 08:30:34 EDT 2025
% 0.10/0.32 % CPUTime :
% 268.19/268.29 % SZS status Unsatisfiable
% 268.19/268.29 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------