%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP413-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n001.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 06:44:00 AM UTC 2025
% Result : Unsatisfiable 66.15s 66.32s
% Output : CNFRefutation 66.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 2
% Syntax : Number of clauses : 55 ( 55 unt; 0 nHn; 3 RR)
% Number of literals : 55 ( 54 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 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 : 177 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c1,axiom,
multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(multiply(X,inverse(Y))),Z))),Y))) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(Z)),Y))) = inverse(multiply(multiply(multiply(inverse(W),W),inverse(multiply(inverse(multiply(inverse(multiply(X,inverse(Y))),inverse(W))),Z))),W)),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(Z)),Y)))) = Z,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(Z,Y)))) = multiply(multiply(multiply(inverse(W),W),inverse(multiply(inverse(multiply(multiply(inverse(Y),Y),inverse(W))),Z))),W),
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c5,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,inverse(multiply(Z,X)))))) = Z,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c7,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,multiply(Z,inverse(multiply(multiply(multiply(inverse(W),W),inverse(V)),W))))) = multiply(inverse(multiply(inverse(multiply(Z,inverse(W))),inverse(Y))),V),
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c8,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)) = multiply(inverse(multiply(inverse(multiply(W,inverse(V))),inverse(Y))),multiply(inverse(multiply(W,inverse(V))),Z)),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c9,plain,
multiply(inverse(multiply(inverse(X),inverse(Y))),multiply(inverse(X),Z)) = multiply(inverse(multiply(W,inverse(Y))),multiply(W,Z)),
inference(equational,[status(thm)],[c1,c8]) ).
cnf(c10,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)) = multiply(inverse(multiply(W,inverse(Y))),multiply(W,Z)),
inference(equational,[status(thm)],[c8,c9]) ).
cnf(c11,plain,
inverse(multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,Z)))),X)) = Z,
inference(equational,[status(thm)],[c1,c2,c8]) ).
cnf(c12,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(multiply(W,Y)),multiply(W,Z)),
inference(equational,[status(thm)],[c10,c11]) ).
cnf(c13,plain,
inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),Z),Y))))) = Z,
inference(equational,[status(thm)],[c4,c11]) ).
cnf(c14,plain,
inverse(multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z))) = inverse(multiply(inverse(multiply(W,inverse(Y))),multiply(W,Z))),
inference(equational,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))) = inverse(multiply(inverse(multiply(W,Y)),multiply(W,Z))),
inference(equational,[status(thm)],[c13,c14]) ).
cnf(c17,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(multiply(W,Y)),multiply(W,V))) = multiply(inverse(multiply(U,Z)),multiply(U,multiply(X,V))),
inference(equational,[status(thm)],[c12]) ).
cnf(c18,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)],[c12]) ).
cnf(c19,plain,
multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,multiply(Y,W))) = multiply(inverse(multiply(V,multiply(U,Z))),multiply(V,multiply(U,W))),
inference(equational,[status(thm)],[c17,c18]) ).
cnf(c23,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),Z),Y)))) = multiply(multiply(multiply(inverse(W),W),inverse(multiply(inverse(multiply(V,inverse(W))),multiply(V,Z)))),W),
inference(equational,[status(thm)],[c3,c11]) ).
cnf(c24,plain,
multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,inverse(Z))))),X) = Z,
inference(equational,[status(thm)],[c3,c23]) ).
cnf(c25,plain,
multiply(inverse(multiply(X,multiply(Y,inverse(multiply(multiply(multiply(inverse(Z),Z),W),Z))))),multiply(X,V)) = multiply(W,multiply(inverse(multiply(Y,inverse(Z))),V)),
inference(equational,[status(thm)],[c11,c12,c23]) ).
cnf(c26,plain,
multiply(X,multiply(inverse(multiply(Y,inverse(Z))),multiply(Y,W))) = multiply(X,multiply(inverse(multiply(V,inverse(Z))),multiply(V,W))),
inference(equational,[status(thm)],[c19,c25]) ).
cnf(c27,plain,
multiply(X,multiply(inverse(multiply(Y,Z)),multiply(Y,W))) = multiply(X,multiply(inverse(multiply(V,Z)),multiply(V,W))),
inference(equational,[status(thm)],[c13,c26]) ).
cnf(c33,plain,
multiply(inverse(multiply(X,Y)),multiply(X,multiply(Z,inverse(multiply(multiply(multiply(inverse(W),W),inverse(V)),W))))) = multiply(inverse(multiply(inverse(multiply(Z,inverse(W))),Y)),V),
inference(equational,[status(thm)],[c7,c11]) ).
cnf(c49,plain,
multiply(X,multiply(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(multiply(Z,inverse(Y))),multiply(Z,X)))),W)) = multiply(inverse(multiply(V,Y)),multiply(V,W)),
inference(equational,[status(thm)],[c11,c12]) ).
cnf(c50,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(Y,Z)),multiply(Y,Z)),
inference(equational,[status(thm)],[c24,c49]) ).
cnf(c51,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c3,c33,c50]) ).
cnf(c52,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(Y),Y)),
inference(equational,[status(thm)],[c15,c50,c51]) ).
cnf(c53,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)) = multiply(inverse(Z),Z),
inference(equational,[status(thm)],[c50,c52]) ).
cnf(c54,plain,
multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))),X) = X,
inference(equational,[status(thm)],[c3,c23,c50]) ).
cnf(c56,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(multiply(W,Y)),multiply(W,Z)),
inference(equational,[status(thm)],[c12,c51]) ).
cnf(c58,plain,
multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(Y),Y))),Z) = Z,
inference(equational,[status(thm)],[c51,c54]) ).
cnf(c59,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(Y),Z),
inference(equational,[status(thm)],[c12,c58]) ).
cnf(c61,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(Y),Z),
inference(equational,[status(thm)],[c56,c58]) ).
cnf(c62,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = Y,
inference(equational,[status(thm)],[c1,c61]) ).
cnf(c63,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(Y),X),
inference(equational,[status(thm)],[c51,c59]) ).
cnf(c72,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(Y),W)) = multiply(inverse(Z),multiply(X,W)),
inference(equational,[status(thm)],[c27,c59]) ).
cnf(c74,plain,
inverse(multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(inverse(X)),Y))),X)) = Y,
inference(equational,[status(thm)],[c11,c58]) ).
cnf(c78,plain,
inverse(multiply(inverse(inverse(X)),inverse(multiply(multiply(multiply(inverse(X),X),Y),X)))) = Y,
inference(equational,[status(thm)],[c13,c58]) ).
cnf(c79,plain,
multiply(inverse(inverse(multiply(multiply(multiply(inverse(X),X),Y),X))),Z) = multiply(Y,multiply(inverse(inverse(X)),Z)),
inference(equational,[status(thm)],[c59,c78]) ).
cnf(c90,plain,
multiply(multiply(inverse(X),X),inverse(multiply(inverse(inverse(X)),inverse(multiply(Y,X))))) = Y,
inference(equational,[status(thm)],[c5,c58]) ).
cnf(c93,plain,
multiply(inverse(inverse(X)),inverse(multiply(multiply(multiply(inverse(X),X),inverse(Y)),X))) = Y,
inference(equational,[status(thm)],[c3,c58]) ).
cnf(c110,plain,
multiply(inverse(inverse(multiply(multiply(multiply(inverse(X),X),Y),Z))),W) = multiply(Y,multiply(inverse(inverse(Z)),W)),
inference(equational,[status(thm)],[c51,c79]) ).
cnf(c112,plain,
inverse(multiply(inverse(inverse(X)),inverse(multiply(multiply(multiply(inverse(Y),Y),Z),X)))) = Z,
inference(equational,[status(thm)],[c53,c63,c78]) ).
cnf(c116,plain,
inverse(multiply(inverse(inverse(X)),inverse(multiply(Y,X)))) = inverse(multiply(inverse(inverse(Z)),inverse(multiply(Y,Z)))),
inference(equational,[status(thm)],[c90,c112]) ).
cnf(c118,plain,
multiply(inverse(inverse(X)),inverse(multiply(Y,X))) = multiply(inverse(inverse(Z)),inverse(multiply(Y,Z))),
inference(equational,[status(thm)],[c93,c116]) ).
cnf(c120,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y))) = multiply(inverse(inverse(Z)),inverse(multiply(inverse(X),Z))),
inference(equational,[status(thm)],[c52,c118]) ).
cnf(c121,plain,
multiply(inverse(X),inverse(multiply(inverse(Y),Y))) = multiply(inverse(inverse(Z)),inverse(multiply(X,Z))),
inference(equational,[status(thm)],[c112,c120]) ).
cnf(c123,plain,
multiply(multiply(multiply(inverse(X),X),inverse(X)),X) = multiply(inverse(inverse(Y)),inverse(Y)),
inference(equational,[status(thm)],[c4,c59,c62,c112,c121]) ).
cnf(c124,plain,
multiply(inverse(X),X) = multiply(multiply(multiply(inverse(Y),Y),inverse(Y)),Y),
inference(equational,[status(thm)],[c2,c59,c72,c93,c110,c123]) ).
cnf(c125,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y))) = X,
inference(equational,[status(thm)],[c93,c124]) ).
cnf(c126,plain,
multiply(multiply(inverse(X),X),inverse(X)) = inverse(X),
inference(equational,[status(thm)],[c90,c125]) ).
cnf(c127,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference(equational,[status(thm)],[c11,c74,c126]) ).
cnf(g1,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(equational,[status(thm)],[c127]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP413-1 : TPTP v9.0.0. Released v2.6.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 08:26:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 66.15/66.32 % SZS status Unsatisfiable
% 66.15/66.32 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------