%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP408-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n013.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 06:43:59 AM UTC 2025
% Result : Unsatisfiable 54.38s 54.51s
% Output : CNFRefutation 54.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 3 RR)
% Number of literals : 40 ( 39 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 2 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 : 131 ( 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,
multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(Y),multiply(inverse(Y),Y))))) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),W)),multiply(inverse(Z),multiply(inverse(Z),Z)))) = multiply(X,inverse(multiply(inverse(W),multiply(inverse(Y),multiply(inverse(Y),Y))))),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(inverse(Z),multiply(inverse(Y),multiply(inverse(Y),Y)))))) = Z,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
multiply(inverse(multiply(X,Y)),multiply(X,multiply(Z,inverse(multiply(inverse(W),multiply(inverse(V),multiply(inverse(V),V))))))) = multiply(inverse(multiply(inverse(multiply(Z,V)),Y)),W),
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(multiply(inverse(multiply(W,V)),Y)),multiply(inverse(multiply(W,V)),Z)),
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c6,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(multiply(W,Y)),multiply(W,Z)),
inference(equational,[status(thm)],[c1,c4,c5]) ).
cnf(c7,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(Y),multiply(inverse(Y),Y)))) = Z,
inference(equational,[status(thm)],[c1,c2,c5]) ).
cnf(c9,plain,
inverse(multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,multiply(Y,inverse(multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),multiply(inverse(X),multiply(inverse(X),X)))))))) = Z,
inference(equational,[status(thm)],[c1,c2,c4,c6]) ).
cnf(c10,plain,
multiply(inverse(multiply(X,Y)),multiply(X,multiply(Z,W))) = multiply(inverse(multiply(inverse(multiply(Z,V)),Y)),multiply(inverse(multiply(U,V)),multiply(U,W))),
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c11,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)],[c5,c6]) ).
cnf(c12,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)],[c10,c11]) ).
cnf(c13,plain,
multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(inverse(multiply(Z,W)),multiply(Z,multiply(inverse(Y),Y)))))) = multiply(inverse(Y),W),
inference(equational,[status(thm)],[c3,c6]) ).
cnf(c14,plain,
inverse(multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(X),multiply(inverse(X),X)))) = inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,multiply(inverse(X),X)))),
inference(equational,[status(thm)],[c7,c13]) ).
cnf(c22,plain,
multiply(X,multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,X))),multiply(inverse(Z),W))) = multiply(inverse(multiply(V,multiply(U,multiply(inverse(Z),Z)))),multiply(V,multiply(U,W))),
inference(equational,[status(thm)],[c7,c12]) ).
cnf(c23,plain,
multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(Z,multiply(inverse(Y),multiply(inverse(Y),Y)))))) = multiply(inverse(multiply(inverse(multiply(W,V)),multiply(W,Z))),multiply(inverse(V),multiply(inverse(V),V))),
inference(equational,[status(thm)],[c3,c7]) ).
cnf(c24,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(Z,multiply(inverse(Y),multiply(inverse(Y),Y))))))) = Z,
inference(equational,[status(thm)],[c7,c23]) ).
cnf(c25,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))) = inverse(multiply(inverse(multiply(W,Y)),multiply(W,Z))),
inference(equational,[status(thm)],[c7,c24]) ).
cnf(c26,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(Z)))),multiply(inverse(Y),multiply(inverse(Y),Y))) = Z,
inference(equational,[status(thm)],[c3,c23]) ).
cnf(c28,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(Z)))),W)),Z) = multiply(inverse(multiply(V,W)),multiply(V,multiply(inverse(Y),multiply(inverse(Y),Y)))),
inference(equational,[status(thm)],[c6,c26]) ).
cnf(c31,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(Y,multiply(Z,multiply(inverse(W),W)))),multiply(Y,multiply(Z,multiply(inverse(W),W)))),
inference(equational,[status(thm)],[c22,c26]) ).
cnf(c32,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c26,c28,c31]) ).
cnf(c35,plain,
multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),Z)) = multiply(inverse(multiply(W,Y)),multiply(W,Z)),
inference(equational,[status(thm)],[c6,c32]) ).
cnf(c37,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(W,Y)),multiply(W,X)),
inference(equational,[status(thm)],[c6,c32]) ).
cnf(c38,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,multiply(inverse(Y),Y)))) = Y,
inference(equational,[status(thm)],[c1,c2,c35]) ).
cnf(c42,plain,
multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z)) = multiply(inverse(multiply(inverse(W),W)),multiply(inverse(Y),X)),
inference(equational,[status(thm)],[c35,c37]) ).
cnf(c45,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)],[c25,c32]) ).
cnf(c48,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,multiply(inverse(Z),Z)))) = Y,
inference(equational,[status(thm)],[c32,c38]) ).
cnf(c50,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = Y,
inference(equational,[status(thm)],[c9,c48]) ).
cnf(c55,plain,
inverse(multiply(inverse(X),multiply(inverse(Y),Y))) = X,
inference(equational,[status(thm)],[c14,c48,c50]) ).
cnf(c56,plain,
inverse(multiply(inverse(X),Y)) = multiply(inverse(Y),X),
inference(equational,[status(thm)],[c13,c48,c55]) ).
cnf(c57,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c50,c55,c56]) ).
cnf(c59,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c1,c50,c55]) ).
cnf(c60,plain,
multiply(X,multiply(inverse(Y),Y)) = X,
inference(equational,[status(thm)],[c42,c50,c55]) ).
cnf(c73,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(Y),Z),
inference(equational,[status(thm)],[c3,c48]) ).
cnf(c75,plain,
multiply(inverse(multiply(inverse(X),Y)),Z) = multiply(inverse(Y),multiply(X,Z)),
inference(equational,[status(thm)],[c22,c59,c60,c73]) ).
cnf(c76,plain,
multiply(multiply(inverse(X),Y),Z) = multiply(inverse(X),multiply(Y,Z)),
inference(equational,[status(thm)],[c45,c59,c73,c75]) ).
cnf(c77,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference(equational,[status(thm)],[c55,c57,c60,c76]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c77]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : GRP408-1 : TPTP v9.0.0. Released v2.6.0.
% 0.02/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n013.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 08:26:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 54.38/54.51 % SZS status Unsatisfiable
% 54.38/54.51 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------