%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP119-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n014.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 06:43:26 AM UTC 2025
% Result : Unsatisfiable 7.10s 7.31s
% Output : CNFRefutation 7.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of clauses : 56 ( 56 unt; 0 nHn; 4 RR)
% Number of literals : 56 ( 55 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(a,multiply(a,multiply(a,a))) != identity,
file('theBenchmark.p',prove_order4) ).
cnf(c1,axiom,
multiply(identity,identity) = identity,
file('theBenchmark.p',single_axiom2) ).
cnf(c2,axiom,
multiply(X,multiply(multiply(X,multiply(multiply(X,X),multiply(Y,Z))),multiply(Z,multiply(Z,Z)))) = Y,
file('theBenchmark.p',single_axiom) ).
cnf(c3,plain,
multiply(X,multiply(multiply(X,multiply(multiply(X,X),identity)),identity)) = identity,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,plain,
multiply(X,multiply(multiply(X,multiply(multiply(X,X),multiply(Y,identity))),identity)) = Y,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c5,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X,identity))),identity)) = X,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c6,plain,
multiply(identity,multiply(multiply(identity,X),identity)) = multiply(identity,multiply(identity,multiply(X,identity))),
inference(equational,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X,identity),identity)))) = X,
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c10,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X,Y))),multiply(Y,multiply(Y,Y)))) = X,
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c12,plain,
multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X),identity),identity))) = X,
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c13,plain,
multiply(multiply(identity,X),identity) = multiply(identity,multiply(X,identity)),
inference(equational,[status(thm)],[c1,c10,c12]) ).
cnf(c14,plain,
multiply(X,multiply(multiply(X,Y),identity)) = multiply(multiply(X,X),multiply(multiply(multiply(X,X),multiply(X,X)),multiply(Y,identity))),
inference(equational,[status(thm)],[c4]) ).
cnf(c15,plain,
multiply(multiply(X,X),multiply(multiply(X,multiply(multiply(X,Y),identity)),identity)) = Y,
inference(equational,[status(thm)],[c4,c14]) ).
cnf(c16,plain,
multiply(multiply(X,multiply(multiply(X,X),identity)),identity) = multiply(multiply(X,X),multiply(multiply(X,identity),identity)),
inference(equational,[status(thm)],[c1,c3,c15]) ).
cnf(c20,plain,
multiply(multiply(X,X),multiply(multiply(X,X),multiply(multiply(X,identity),identity))) = X,
inference(equational,[status(thm)],[c15,c16]) ).
cnf(c21,plain,
multiply(identity,multiply(identity,multiply(multiply(X,identity),identity))) = multiply(multiply(identity,multiply(identity,multiply(X,Y))),multiply(Y,multiply(Y,Y))),
inference(equational,[status(thm)],[c1,c10,c13,c15]) ).
cnf(c22,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(identity,X),Y))),multiply(Y,multiply(Y,Y))) = X,
inference(equational,[status(thm)],[c12,c21]) ).
cnf(c23,plain,
multiply(X,multiply(multiply(X,multiply(multiply(X,X),multiply(identity,multiply(Y,identity)))),identity)) = multiply(identity,Y),
inference(equational,[status(thm)],[c4,c13]) ).
cnf(c24,plain,
multiply(X,multiply(multiply(X,multiply(multiply(X,X),Y)),identity)) = multiply(identity,multiply(identity,multiply(identity,multiply(Y,identity)))),
inference(equational,[status(thm)],[c5,c23]) ).
cnf(c25,plain,
multiply(multiply(X,multiply(multiply(X,X),Y)),identity) = multiply(multiply(X,X),multiply(multiply(X,Y),identity)),
inference(equational,[status(thm)],[c7,c13,c15,c24]) ).
cnf(c26,plain,
multiply(X,multiply(multiply(X,X),multiply(multiply(X,Y),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(Y,identity)))),
inference(equational,[status(thm)],[c1,c4,c23,c25]) ).
cnf(c29,plain,
multiply(multiply(X,X),multiply(multiply(X,multiply(Y,identity)),identity)) = multiply(multiply(X,multiply(multiply(X,X),multiply(Y,Z))),multiply(Z,multiply(Z,Z))),
inference(equational,[status(thm)],[c2,c15]) ).
cnf(c30,plain,
multiply(multiply(X,multiply(multiply(X,X),multiply(multiply(X,Y),Z))),multiply(Z,multiply(Z,Z))) = Y,
inference(equational,[status(thm)],[c15,c29]) ).
cnf(c32,plain,
multiply(multiply(X,multiply(multiply(X,X),multiply(identity,Y))),multiply(Y,multiply(Y,Y))) = multiply(multiply(X,X),multiply(multiply(X,identity),identity)),
inference(equational,[status(thm)],[c1,c29]) ).
cnf(c37,plain,
multiply(multiply(multiply(X,X),multiply(X,X)),multiply(multiply(multiply(X,X),multiply(Y,identity)),identity)) = multiply(multiply(X,multiply(multiply(X,Y),identity)),identity),
inference(equational,[status(thm)],[c15]) ).
cnf(c42,plain,
multiply(X,multiply(multiply(multiply(X,identity),identity),multiply(multiply(multiply(X,identity),identity),multiply(multiply(X,identity),identity)))) = identity,
inference(equational,[status(thm)],[c1,c10,c21]) ).
cnf(c47,plain,
multiply(multiply(multiply(X,identity),identity),multiply(multiply(multiply(X,identity),identity),multiply(multiply(X,identity),identity))) = multiply(multiply(X,X),multiply(multiply(X,identity),identity)),
inference(equational,[status(thm)],[c30,c32,c42]) ).
cnf(c48,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(X,X),Y),identity)))) = multiply(X,multiply(multiply(X,X),multiply(multiply(X,X),multiply(multiply(X,Y),identity)))),
inference(equational,[status(thm)],[c25,c26]) ).
cnf(c49,plain,
multiply(identity,multiply(multiply(X,multiply(X,X)),multiply(multiply(X,multiply(X,X)),multiply(X,multiply(X,X))))) = multiply(identity,multiply(identity,X)),
inference(equational,[status(thm)],[c1,c22,c32]) ).
cnf(c50,plain,
multiply(multiply(X,multiply(X,X)),multiply(multiply(X,multiply(X,X)),multiply(X,multiply(X,X)))) = multiply(identity,X),
inference(equational,[status(thm)],[c22,c49]) ).
cnf(c51,plain,
multiply(multiply(identity,multiply(identity,multiply(multiply(identity,X),multiply(Y,multiply(Y,Y))))),multiply(identity,Y)) = X,
inference(equational,[status(thm)],[c22,c50]) ).
cnf(c52,plain,
multiply(multiply(identity,X),multiply(identity,Y)) = multiply(identity,multiply(X,Y)),
inference(equational,[status(thm)],[c10,c51]) ).
cnf(c53,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(X,identity),identity))),Y)) = multiply(X,multiply(identity,Y)),
inference(equational,[status(thm)],[c7,c52]) ).
cnf(c55,plain,
multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X,multiply(X,X)))),X)) = identity,
inference(equational,[status(thm)],[c1,c51,c52]) ).
cnf(c56,plain,
multiply(multiply(identity,multiply(identity,multiply(X,multiply(X,X)))),X) = identity,
inference(equational,[status(thm)],[c51,c52,c55]) ).
cnf(c57,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X,multiply(Y,multiply(Y,Y)))),Y))) = X,
inference(equational,[status(thm)],[c51,c52]) ).
cnf(c60,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,X),Y))) = multiply(Z,multiply(multiply(Z,Z),multiply(multiply(Z,X),Y))),
inference(equational,[status(thm)],[c30,c57]) ).
cnf(c61,plain,
multiply(X,multiply(multiply(X,X),multiply(multiply(X,identity),Y))) = multiply(identity,multiply(identity,multiply(identity,Y))),
inference(equational,[status(thm)],[c1,c60]) ).
cnf(c62,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X),multiply(Y,multiply(Y,Y)))),Y)) = X,
inference(equational,[status(thm)],[c51,c52]) ).
cnf(c63,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,X),multiply(multiply(X,identity),identity)))) = multiply(X,X),
inference(equational,[status(thm)],[c20,c60]) ).
cnf(c64,plain,
multiply(identity,multiply(multiply(multiply(X,X),identity),identity)) = multiply(multiply(identity,X),multiply(multiply(X,identity),identity)),
inference(equational,[status(thm)],[c1,c7,c13,c37,c63]) ).
cnf(c65,plain,
multiply(multiply(identity,multiply(X,multiply(identity,Y))),multiply(Y,multiply(Y,Y))) = multiply(identity,multiply(multiply(X,identity),identity)),
inference(equational,[status(thm)],[c22,c53]) ).
cnf(c67,plain,
multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(X,identity),identity)),Y))) = multiply(X,multiply(identity,multiply(identity,Y))),
inference(equational,[status(thm)],[c52,c53]) ).
cnf(c76,plain,
multiply(multiply(X,multiply(identity,multiply(identity,multiply(identity,multiply(Y,identity))))),identity) = multiply(multiply(X,identity),Y),
inference(equational,[status(thm)],[c13,c15,c37,c61]) ).
cnf(c77,plain,
multiply(multiply(X,Y),identity) = multiply(multiply(X,identity),multiply(Y,identity)),
inference(equational,[status(thm)],[c7,c76]) ).
cnf(c83,plain,
multiply(multiply(X,identity),multiply(multiply(Y,identity),multiply(Z,identity))) = multiply(multiply(X,multiply(Y,Z)),identity),
inference(equational,[status(thm)],[c77]) ).
cnf(c89,plain,
multiply(identity,multiply(multiply(multiply(X,identity),identity),multiply(multiply(X,identity),identity))) = multiply(multiply(identity,X),multiply(multiply(X,identity),identity)),
inference(equational,[status(thm)],[c1,c64,c77,c83]) ).
cnf(c90,plain,
multiply(identity,multiply(multiply(identity,multiply(X,multiply(Y,multiply(Y,Y)))),Y)) = multiply(identity,multiply(multiply(identity,multiply(X,multiply(Z,multiply(Z,Z)))),Z)),
inference(equational,[status(thm)],[c57,c62]) ).
cnf(c91,plain,
multiply(identity,multiply(multiply(X,multiply(X,X)),multiply(identity,multiply(multiply(X,identity),identity)))) = identity,
inference(equational,[status(thm)],[c1,c52,c56,c63,c67,c89,c90]) ).
cnf(c93,plain,
multiply(identity,multiply(multiply(multiply(X,multiply(X,X)),identity),identity)) = multiply(identity,multiply(multiply(X,X),multiply(multiply(X,identity),identity))),
inference(equational,[status(thm)],[c47,c65,c91]) ).
cnf(c94,plain,
multiply(multiply(X,multiply(X,X)),identity) = multiply(X,multiply(multiply(X,X),identity)),
inference(equational,[status(thm)],[c1,c10,c13,c15,c48,c93]) ).
cnf(c95,plain,
multiply(multiply(X,identity),multiply(multiply(X,X),identity)) = multiply(X,multiply(multiply(X,X),identity)),
inference(equational,[status(thm)],[c77,c94]) ).
cnf(c96,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c10,c95]) ).
cnf(c99,plain,
multiply(X,multiply(X,multiply(X,X))) = identity,
inference(equational,[status(thm)],[c1,c24,c94,c96]) ).
cnf(g1,plain,
multiply(a,multiply(a,multiply(a,a))) = identity,
inference(equational,[status(thm)],[c99]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP119-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 08:08:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 7.10/7.31 % SZS status Unsatisfiable
% 7.10/7.31 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------