%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP515-1 : TPTP v9.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n006.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 06:44:14 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.45s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% 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 : 8 ( 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 : 39 ( 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,multiply(multiply(Y,Z),inverse(multiply(X,Z)))) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c2,plain,
multiply(X,multiply(Y,inverse(multiply(X,multiply(multiply(Y,Z),inverse(multiply(W,Z))))))) = W,
inference(equational,[status(thm)],[c1]) ).
cnf(c3,plain,
multiply(X,multiply(Y,inverse(Y))) = X,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
multiply(X,multiply(Y,inverse(X))) = Y,
inference(equational,[status(thm)],[c2,c3]) ).
cnf(c5,plain,
multiply(multiply(X,Y),multiply(Z,inverse(multiply(Z,Y)))) = X,
inference(equational,[status(thm)],[c2,c4]) ).
cnf(c6,plain,
multiply(multiply(X,Y),multiply(Z,inverse(X))) = multiply(Z,Y),
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,plain,
multiply(X,multiply(Y,inverse(Z))) = multiply(Y,multiply(X,inverse(Z))),
inference(equational,[status(thm)],[c4,c6]) ).
cnf(c8,plain,
multiply(X,multiply(multiply(Y,Z),inverse(Y))) = multiply(X,Z),
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c9,plain,
multiply(multiply(X,Y),Z) = multiply(multiply(X,Z),Y),
inference(equational,[status(thm)],[c6,c8]) ).
cnf(c12,plain,
multiply(X,multiply(Y,multiply(multiply(Z,inverse(Y)),inverse(X)))) = Z,
inference(equational,[status(thm)],[c1,c4,c7,c9]) ).
cnf(c13,plain,
multiply(multiply(X,Y),inverse(Y)) = X,
inference(equational,[status(thm)],[c3,c9,c12]) ).
cnf(c14,plain,
multiply(X,Y) = multiply(Y,X),
inference(equational,[status(thm)],[c4,c13]) ).
cnf(c15,plain,
multiply(multiply(X,inverse(X)),Y) = Y,
inference(equational,[status(thm)],[c1,c12]) ).
cnf(c16,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c13,c15]) ).
cnf(c21,plain,
multiply(X,multiply(Y,Z)) = multiply(Y,multiply(X,Z)),
inference(equational,[status(thm)],[c7,c16]) ).
cnf(g1,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(equational,[status(thm)],[c14,c21]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP515-1 : TPTP v9.0.0. Released v2.6.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 14 08:31:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.45 % SZS status Unsatisfiable
% 0.18/0.45 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------