%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP412-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n003.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 51.03s 51.20s
% Output : CNFRefutation 51.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 3 RR)
% Number of literals : 17 ( 16 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 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 : 54 ( 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(X,inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(multiply(X,inverse(Y))),Z))),Y))) = Z,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
inverse(multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(inverse(multiply(Y,inverse(Z))),inverse(X))),W))),X)) = multiply(Y,inverse(multiply(multiply(multiply(inverse(Z),Z),inverse(W)),Z))),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(Z)),Y)))) = Z,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c7,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,multiply(Z,inverse(multiply(multiply(multiply(inverse(W),W),inverse(V)),W))))) = multiply(inverse(multiply(inverse(multiply(Z,inverse(W))),inverse(Y))),V),
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c8,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)) = multiply(inverse(multiply(inverse(multiply(W,inverse(V))),inverse(Y))),multiply(inverse(multiply(W,inverse(V))),Z)),
inference(equational,[status(thm)],[c1,c7]) ).
cnf(c9,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,Z)) = multiply(inverse(multiply(W,inverse(Y))),multiply(W,Z)),
inference(equational,[status(thm)],[c1,c7,c8]) ).
cnf(c10,plain,
inverse(multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,Z)))),X)) = Z,
inference(equational,[status(thm)],[c1,c2,c8]) ).
cnf(c11,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(multiply(W,Y)),multiply(W,Z)),
inference(equational,[status(thm)],[c9,c10]) ).
cnf(c32,plain,
multiply(inverse(multiply(X,inverse(Y))),multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),Z),Y)))) = multiply(multiply(multiply(inverse(W),W),inverse(multiply(inverse(multiply(V,inverse(W))),multiply(V,Z)))),W),
inference(equational,[status(thm)],[c3,c10]) ).
cnf(c33,plain,
multiply(multiply(multiply(inverse(X),X),inverse(multiply(inverse(multiply(Y,inverse(X))),multiply(Y,inverse(Z))))),X) = Z,
inference(equational,[status(thm)],[c3,c32]) ).
cnf(c37,plain,
multiply(inverse(multiply(inverse(multiply(X,inverse(Y))),Z)),W) = multiply(inverse(multiply(V,Z)),multiply(V,multiply(X,inverse(multiply(multiply(multiply(inverse(Y),Y),inverse(W)),Y))))),
inference(equational,[status(thm)],[c7,c10]) ).
cnf(c40,plain,
multiply(X,multiply(multiply(multiply(inverse(Y),Y),inverse(multiply(inverse(multiply(Z,inverse(Y))),multiply(Z,X)))),W)) = multiply(inverse(multiply(V,Y)),multiply(V,W)),
inference(equational,[status(thm)],[c10,c11]) ).
cnf(c41,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(Y,Z)),multiply(Y,Z)),
inference(equational,[status(thm)],[c33,c40]) ).
cnf(c42,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference(equational,[status(thm)],[c3,c37,c41]) ).
cnf(g1,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(equational,[status(thm)],[c42]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP412-1 : TPTP v9.0.0. Released v2.6.0.
% 0.00/0.09 % Command : run_Leo-III %s %d THM
% 0.08/0.29 % Computer : n003.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Mon Jul 14 08:26:19 EDT 2025
% 0.08/0.29 % CPUTime :
% 51.03/51.20 % SZS status Unsatisfiable
% 51.03/51.20 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------