%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP439-1 : 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 06:44:03 AM UTC 2025
% Result : Unsatisfiable 2.44s 2.64s
% Output : CNFRefutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 3 RR)
% Number of literals : 23 ( 22 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 : 86 ( 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,
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(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(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(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(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(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c44]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP439-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.11 % Command : run_Leo-III %s %d THM
% 0.12/0.31 % Computer : n001.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Mon Jul 14 08:28:04 EDT 2025
% 0.12/0.31 % CPUTime :
% 2.44/2.64 % SZS status Unsatisfiable
% 2.44/2.64 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------