%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP417-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n016.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 63.60s 63.73s
% Output : CNFRefutation 63.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 2
% Syntax : Number of clauses : 48 ( 48 unt; 0 nHn; 3 RR)
% Number of literals : 48 ( 47 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 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 : 132 ( 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(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,inverse(Z)))),inverse(multiply(inverse(X),X)))))) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,Z))),inverse(multiply(inverse(X),X)))))) = multiply(W,inverse(multiply(inverse(multiply(inverse(multiply(V,W)),multiply(V,inverse(Z)))),inverse(multiply(inverse(W),W))))),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
inverse(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,Z))),inverse(multiply(inverse(X),X))))))) = Z,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),multiply(Y,inverse(inverse(Z))))),inverse(multiply(inverse(X),X))))) = Z,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c5,plain,
inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),Z)),inverse(multiply(inverse(X),X)))))) = multiply(inverse(multiply(inverse(multiply(W,Y)),multiply(W,inverse(inverse(Z))))),inverse(multiply(inverse(Y),Y))),
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c6,plain,
multiply(X,inverse(inverse(multiply(Y,inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),inverse(multiply(inverse(Y),Y)))))))) = Z,
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c7,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(inverse(multiply(Y,inverse(Z))))))),inverse(multiply(inverse(Y),Y))) = Z,
inference(equational,[status(thm)],[c1,c5]) ).
cnf(c9,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(inverse(multiply(Y,Z)))))),inverse(multiply(inverse(Y),Y)))) = Z,
inference(equational,[status(thm)],[c3,c5]) ).
cnf(c14,plain,
inverse(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),Z)),inverse(multiply(inverse(X),X))))))) = inverse(multiply(inverse(multiply(inverse(multiply(W,Y)),multiply(W,inverse(inverse(Z))))),inverse(multiply(inverse(Y),Y)))),
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c15,plain,
inverse(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,X)),Z)),inverse(multiply(inverse(X),X))))))) = inverse(inverse(multiply(W,inverse(multiply(inverse(multiply(inverse(multiply(Y,W)),Z)),inverse(multiply(inverse(W),W))))))),
inference(equational,[status(thm)],[c5,c14]) ).
cnf(c19,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(inverse(multiply(Y,Z)))))),inverse(multiply(inverse(Y),Y))) = multiply(inverse(multiply(inverse(multiply(W,V)),multiply(W,inverse(inverse(multiply(V,Z)))))),inverse(multiply(inverse(V),V))),
inference(equational,[status(thm)],[c7,c9]) ).
cnf(c20,plain,
multiply(X,inverse(inverse(multiply(Y,inverse(multiply(inverse(Z),inverse(multiply(inverse(Y),Y)))))))) = inverse(inverse(multiply(W,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),W)),Z)),inverse(multiply(inverse(W),W))))))),
inference(equational,[status(thm)],[c6]) ).
cnf(c21,plain,
multiply(inverse(multiply(X,Y)),multiply(X,inverse(inverse(multiply(Y,inverse(multiply(inverse(Z),inverse(multiply(inverse(Y),Y))))))))) = Z,
inference(equational,[status(thm)],[c6,c20]) ).
cnf(c22,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(multiply(W,Y)),multiply(W,Z)),
inference(equational,[status(thm)],[c3,c21]) ).
cnf(c26,plain,
multiply(X,multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,inverse(inverse(multiply(Z,X)))))),W)) = multiply(inverse(multiply(V,inverse(multiply(inverse(Z),Z)))),multiply(V,W)),
inference(equational,[status(thm)],[c9,c19,c22]) ).
cnf(c27,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(Y,inverse(multiply(inverse(Z),Z)))),multiply(Y,inverse(multiply(inverse(Z),Z)))),
inference(equational,[status(thm)],[c7,c26]) ).
cnf(c28,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c7,c27]) ).
cnf(c31,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(W,Y)),multiply(W,X)),
inference(equational,[status(thm)],[c22,c28]) ).
cnf(c32,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(multiply(inverse(Z),Y)),multiply(inverse(W),W)),
inference(equational,[status(thm)],[c28,c31]) ).
cnf(c37,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Y)) = multiply(inverse(multiply(inverse(Z),Z)),multiply(inverse(W),W)),
inference(equational,[status(thm)],[c28,c32]) ).
cnf(c41,plain,
inverse(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(X),X))))))) = X,
inference(equational,[status(thm)],[c6,c20,c28]) ).
cnf(c50,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(Y),Y)))),multiply(X,inverse(multiply(inverse(Z),Z)))) = multiply(inverse(W),W),
inference(equational,[status(thm)],[c27,c28]) ).
cnf(c51,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(Y),Y)),
inference(equational,[status(thm)],[c6,c20,c41,c50]) ).
cnf(c52,plain,
multiply(X,inverse(multiply(inverse(Y),Y))) = multiply(X,inverse(multiply(inverse(Z),Z))),
inference(equational,[status(thm)],[c6,c41,c50]) ).
cnf(c59,plain,
multiply(X,inverse(multiply(inverse(multiply(inverse(Y),Y)),multiply(inverse(Z),Z)))) = multiply(X,inverse(multiply(inverse(W),W))),
inference(equational,[status(thm)],[c51,c52]) ).
cnf(c62,plain,
inverse(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(Z),Z))))))) = X,
inference(equational,[status(thm)],[c28,c41]) ).
cnf(c63,plain,
inverse(inverse(multiply(inverse(X),X))) = inverse(inverse(multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(Z),Z))))),
inference(equational,[status(thm)],[c28,c62]) ).
cnf(c64,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(inverse(Y),Y)),inverse(multiply(inverse(Z),Z))),
inference(equational,[status(thm)],[c4,c63]) ).
cnf(c65,plain,
multiply(inverse(X),X) = inverse(multiply(inverse(Y),Y)),
inference(equational,[status(thm)],[c6,c62,c64]) ).
cnf(c74,plain,
inverse(inverse(multiply(X,inverse(multiply(inverse(Y),Y))))) = X,
inference(equational,[status(thm)],[c3,c15,c64]) ).
cnf(c75,plain,
inverse(inverse(multiply(X,multiply(inverse(Y),Y)))) = X,
inference(equational,[status(thm)],[c65,c74]) ).
cnf(c77,plain,
inverse(multiply(inverse(X),inverse(multiply(inverse(Y),Y)))) = X,
inference(equational,[status(thm)],[c1,c64]) ).
cnf(c78,plain,
multiply(X,multiply(inverse(X),Y)) = multiply(Y,multiply(inverse(Z),Z)),
inference(equational,[status(thm)],[c31,c77]) ).
cnf(c79,plain,
inverse(multiply(inverse(X),multiply(inverse(Y),Y))) = X,
inference(equational,[status(thm)],[c65,c77]) ).
cnf(c80,plain,
multiply(inverse(inverse(X)),inverse(multiply(inverse(Y),Y))) = X,
inference(equational,[status(thm)],[c4,c64]) ).
cnf(c81,plain,
multiply(inverse(inverse(X)),multiply(inverse(Y),Y)) = X,
inference(equational,[status(thm)],[c59,c79,c80]) ).
cnf(c82,plain,
inverse(inverse(multiply(X,multiply(inverse(X),Y)))) = Y,
inference(equational,[status(thm)],[c75,c78]) ).
cnf(c83,plain,
multiply(X,multiply(inverse(X),inverse(inverse(Y)))) = Y,
inference(equational,[status(thm)],[c78,c81]) ).
cnf(c87,plain,
multiply(inverse(inverse(inverse(multiply(X,Y)))),X) = inverse(Y),
inference(equational,[status(thm)],[c21,c77,c79]) ).
cnf(c88,plain,
inverse(multiply(inverse(X),Y)) = multiply(inverse(Y),X),
inference(equational,[status(thm)],[c82,c87]) ).
cnf(c89,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference(equational,[status(thm)],[c79,c88]) ).
cnf(c90,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c83,c88,c89]) ).
cnf(c91,plain,
multiply(X,inverse(X)) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c37,c88,c89,c90]) ).
cnf(c93,plain,
inverse(multiply(X,inverse(X))) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c64,c80,c87,c88,c91]) ).
cnf(c96,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c20,c79,c88,c89,c90,c93]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c96]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP417-1 : TPTP v9.0.0. Released v2.6.0.
% 0.00/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n016.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 08:26:49 EDT 2025
% 0.11/0.32 % CPUTime :
% 63.60/63.73 % SZS status Unsatisfiable
% 63.60/63.73 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------