%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP409-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n011.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 0.49s 0.70s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 3 RR)
% Number of literals : 12 ( 11 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 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 : 33 ( 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,
multiply(multiply(inverse(multiply(X,inverse(multiply(Y,Z)))),multiply(X,inverse(Z))),inverse(multiply(inverse(Z),Z))) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
multiply(multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(inverse(multiply(inverse(Z),Z))))),inverse(multiply(inverse(inverse(multiply(inverse(Z),Z))),inverse(multiply(inverse(Z),Z))))) = multiply(inverse(multiply(W,inverse(multiply(Y,Z)))),multiply(W,inverse(Z))),
inference(equational,[status(thm)],[c1]) ).
cnf(c4,plain,
multiply(inverse(multiply(X,inverse(multiply(multiply(Y,inverse(multiply(inverse(Z),Z))),Z)))),multiply(X,inverse(Z))) = Y,
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c5,plain,
multiply(inverse(multiply(X,inverse(multiply(Y,Z)))),multiply(X,inverse(Z))) = multiply(inverse(multiply(W,inverse(multiply(Y,Z)))),multiply(W,inverse(Z))),
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c6,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(Z,inverse(W))))) = multiply(inverse(multiply(V,inverse(Y))),multiply(V,inverse(multiply(Z,inverse(W))))),
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c7,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(Z))) = multiply(inverse(multiply(W,inverse(Y))),multiply(W,inverse(Z))),
inference(equational,[status(thm)],[c1,c6]) ).
cnf(c9,plain,
multiply(inverse(multiply(multiply(inverse(multiply(X,inverse(multiply(Y,Z)))),multiply(X,inverse(Z))),inverse(W))),Y) = multiply(inverse(multiply(V,inverse(W))),multiply(V,inverse(multiply(inverse(Z),Z)))),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c10,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)],[c1,c9]) ).
cnf(c11,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c1,c9,c10]) ).
cnf(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c11]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : GRP409-1 : TPTP v9.0.0. Released v2.6.0.
% 0.05/0.10 % Command : run_Leo-III %s %d THM
% 0.09/0.30 % Computer : n011.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Jul 14 08:26:34 EDT 2025
% 0.09/0.30 % CPUTime :
% 0.49/0.70 % SZS status Unsatisfiable
% 0.49/0.70 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------