%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP415-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n007.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 60.86s 61.07s
% Output : CNFRefutation 60.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 3 RR)
% Number of literals : 18 ( 17 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 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,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(c18,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,c18,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(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c28]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : GRP415-1 : TPTP v9.0.0. Released v2.6.0.
% 0.00/0.08 % Command : run_Leo-III %s %d THM
% 0.07/0.27 % Computer : n007.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Mon Jul 14 08:26:34 EDT 2025
% 0.07/0.27 % CPUTime :
% 60.86/61.07 % SZS status Unsatisfiable
% 60.86/61.07 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------