%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP118-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:18 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.43s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 2
% Syntax : Number of clauses : 130 ( 130 unt; 0 nHn; 3 RR)
% Number of literals : 130 ( 129 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; 4 con; 0-2 aty)
% Number of variables : 262 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_order3) ).
cnf(c2,axiom,
multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c3,plain,
multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X3),X2)),multiply(identity,multiply(X2,X2)))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X3 = multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X3),X2)),multiply(identity,multiply(X2,X2)))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(X3,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))))) = multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X3),X2)),multiply(identity,multiply(X2,X2)))),multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
multiply(X4,multiply(X3,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(X4,multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X3),X2)),multiply(identity,multiply(X2,X2)))),multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(X4,multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X3),X2)),multiply(identity,multiply(X2,X2)))),multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(multiply(X4,X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
multiply(X4,multiply(X3,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c6,c7]) ).
cnf(c9,plain,
multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X3,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X3),X4)),multiply(identity,multiply(X4,X4)))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c11,plain,
X4 = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X4),X2)),multiply(identity,multiply(X2,X2)))),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(X4,identity) = multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X4),X2)),multiply(identity,multiply(X2,X2)))),identity),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(multiply(X5,identity),X4) = multiply(multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X5),X2)),multiply(identity,multiply(X2,X2)))),identity),X4),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(multiply(X4,X3),multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(multiply(multiply(X4,X3),identity),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c15,plain,
multiply(multiply(multiply(X4,X3),identity),X2) = multiply(multiply(X4,X3),multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(X4,multiply(X3,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))),multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))))))) = multiply(multiply(X4,X3),multiply(identity,X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c17,plain,
multiply(multiply(X4,X3),multiply(identity,X2)) = multiply(X4,multiply(X3,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))),multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))))))),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))),multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c19,plain,
multiply(X3,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))),multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2)))))) = multiply(X3,X2),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(X4,multiply(X3,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))),multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))))))) = multiply(X4,multiply(X3,X2)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(multiply(X4,X3),multiply(identity,X2)) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c17,c20]) ).
cnf(c22,plain,
multiply(multiply(X4,X3),multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(X4,multiply(X3,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(multiply(X4,X3),multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c22,c8]) ).
cnf(c24,plain,
multiply(multiply(multiply(X4,X3),identity),X2) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c15,c23]) ).
cnf(c25,plain,
multiply(multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X5),X2)),multiply(identity,multiply(X2,X2)))),identity),X4) = multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X5),X2)),multiply(identity,multiply(X2,X2)))),X4),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X4),X2)),multiply(identity,multiply(X2,X2)))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c27,plain,
multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X5),X2)),multiply(identity,multiply(X2,X2)))),X4) = multiply(X5,X4),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X5),X2)),multiply(identity,multiply(X2,X2)))),identity),X4) = multiply(X5,X4),
inference(transitivity,[status(thm)],[c25,c27]) ).
cnf(c29,plain,
multiply(multiply(X3,identity),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c13,c28]) ).
cnf(c30,plain,
multiply(multiply(identity,identity),X2) = multiply(identity,X2),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(identity,X2) = multiply(multiply(identity,identity),X2),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(multiply(identity,identity),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c33,plain,
multiply(multiply(identity,identity),X2) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))) = multiply(identity,multiply(multiply(X2,X2),multiply(X2,X2))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c35,plain,
multiply(identity,multiply(multiply(X2,X2),multiply(X2,X2))) = multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(X4,identity)),X2)),multiply(identity,multiply(X2,X2)))) = multiply(X4,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c37,plain,
multiply(X4,identity) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(X4,identity)),X2)),multiply(identity,multiply(X2,X2)))),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
multiply(X4,multiply(multiply(X3,identity),multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(multiply(X4,multiply(X3,identity)),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c39,plain,
multiply(multiply(X4,multiply(X3,identity)),X2) = multiply(X4,multiply(multiply(X3,identity),multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
multiply(multiply(X3,identity),multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))))) = multiply(X3,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))))),
inference(substitution,[status(thm)],[c29]) ).
cnf(c41,plain,
multiply(X4,multiply(multiply(X3,identity),multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(X4,multiply(X3,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
multiply(X4,multiply(multiply(X3,identity),multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c41,c8]) ).
cnf(c43,plain,
multiply(multiply(X4,multiply(X3,identity)),X2) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c39,c42]) ).
cnf(c44,plain,
multiply(multiply(X3,multiply(X4,identity)),X2) = multiply(multiply(X3,X4),X2),
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(X3,multiply(multiply(X3,multiply(X4,identity)),X2)) = multiply(X3,multiply(multiply(X3,X4),X2)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
multiply(multiply(X3,multiply(multiply(X3,multiply(X4,identity)),X2)),multiply(identity,multiply(X2,X2))) = multiply(multiply(X3,multiply(multiply(X3,X4),X2)),multiply(identity,multiply(X2,X2))),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(X4,identity)),X2)),multiply(identity,multiply(X2,X2)))) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X4),X2)),multiply(identity,multiply(X2,X2)))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X4),X2)),multiply(identity,multiply(X2,X2)))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c49,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(X4,identity)),X2)),multiply(identity,multiply(X2,X2)))) = X4,
inference(transitivity,[status(thm)],[c47,c48]) ).
cnf(c50,plain,
multiply(X2,identity) = X2,
inference(transitivity,[status(thm)],[c37,c49]) ).
cnf(c51,plain,
X2 = multiply(X2,identity),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(X3,X2) = multiply(X3,multiply(X2,identity)),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
multiply(X3,multiply(X3,X2)) = multiply(X3,multiply(X3,multiply(X2,identity))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
multiply(X3,multiply(X3,multiply(X3,X2))) = multiply(X3,multiply(X3,multiply(X3,multiply(X2,identity)))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(multiply(X3,X2),multiply(identity,identity)) = multiply(X3,multiply(X2,identity)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c56,plain,
multiply(X3,multiply(X2,identity)) = multiply(multiply(X3,X2),multiply(identity,identity)),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(X3,multiply(X3,multiply(X2,identity))) = multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
multiply(X3,multiply(X3,multiply(X3,multiply(X2,identity)))) = multiply(X3,multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
multiply(multiply(X3,multiply(X3,X2)),multiply(identity,multiply(identity,identity))) = multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c60,plain,
multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))) = multiply(multiply(X3,multiply(X3,X2)),multiply(identity,multiply(identity,identity))),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
multiply(X3,multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity)))) = multiply(X3,multiply(multiply(X3,multiply(X3,X2)),multiply(identity,multiply(identity,identity)))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
multiply(multiply(X3,X2),identity) = multiply(X3,X2),
inference(substitution,[status(thm)],[c50]) ).
cnf(c63,plain,
multiply(X3,X2) = multiply(multiply(X3,X2),identity),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
multiply(X3,multiply(X3,X2)) = multiply(X3,multiply(multiply(X3,X2),identity)),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
multiply(multiply(X3,multiply(X3,X2)),multiply(identity,multiply(identity,identity))) = multiply(multiply(X3,multiply(multiply(X3,X2),identity)),multiply(identity,multiply(identity,identity))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(X3,multiply(multiply(X3,multiply(X3,X2)),multiply(identity,multiply(identity,identity)))) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X2),identity)),multiply(identity,multiply(identity,identity)))),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X2),identity)),multiply(identity,multiply(identity,identity)))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c68,plain,
multiply(X3,multiply(multiply(X3,multiply(X3,X2)),multiply(identity,multiply(identity,identity)))) = X2,
inference(transitivity,[status(thm)],[c66,c67]) ).
cnf(c69,plain,
multiply(X3,multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity)))) = X2,
inference(transitivity,[status(thm)],[c61,c68]) ).
cnf(c70,plain,
multiply(X3,multiply(X3,multiply(X3,multiply(X2,identity)))) = X2,
inference(transitivity,[status(thm)],[c58,c69]) ).
cnf(c71,plain,
multiply(X3,multiply(X3,multiply(X3,X2))) = X2,
inference(transitivity,[status(thm)],[c54,c70]) ).
cnf(c72,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(multiply(identity,identity),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c75,plain,
multiply(multiply(identity,identity),X2) = multiply(identity,X2),
inference(substitution,[status(thm)],[c29]) ).
cnf(c76,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(identity,X2),
inference(transitivity,[status(thm)],[c74,c75]) ).
cnf(c77,plain,
multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))) = multiply(identity,X2),
inference(transitivity,[status(thm)],[c73,c76]) ).
cnf(c78,plain,
multiply(identity,multiply(multiply(X2,X2),multiply(X2,X2))) = multiply(identity,X2),
inference(transitivity,[status(thm)],[c35,c77]) ).
cnf(c79,plain,
multiply(identity,X2) = multiply(identity,multiply(multiply(X2,X2),multiply(X2,X2))),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
multiply(identity,multiply(identity,X2)) = multiply(identity,multiply(identity,multiply(multiply(X2,X2),multiply(X2,X2)))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
multiply(multiply(X3,multiply(X3,X3)),multiply(identity,X2)) = multiply(X3,multiply(multiply(X3,X3),X2)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c82,plain,
multiply(X3,multiply(multiply(X3,X3),X2)) = multiply(multiply(X3,multiply(X3,X3)),multiply(identity,X2)),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
X2 = multiply(X2,identity),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c84,plain,
multiply(X2,X2) = multiply(X2,multiply(X2,identity)),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
multiply(X2,multiply(X2,X2)) = multiply(X2,multiply(X2,multiply(X2,identity))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
multiply(X2,multiply(X2,multiply(X2,identity))) = identity,
inference(substitution,[status(thm)],[c71]) ).
cnf(c87,plain,
multiply(X2,multiply(X2,X2)) = identity,
inference(transitivity,[status(thm)],[c85,c86]) ).
cnf(c88,plain,
multiply(multiply(X3,multiply(X3,X3)),multiply(identity,X2)) = multiply(identity,multiply(identity,X2)),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
multiply(X3,multiply(multiply(X3,X3),X2)) = multiply(identity,multiply(identity,X2)),
inference(transitivity,[status(thm)],[c82,c88]) ).
cnf(c90,plain,
multiply(X2,multiply(multiply(X2,X2),multiply(multiply(X2,X2),multiply(X2,X2)))) = multiply(identity,multiply(identity,multiply(multiply(X2,X2),multiply(X2,X2)))),
inference(substitution,[status(thm)],[c89]) ).
cnf(c91,plain,
multiply(identity,multiply(identity,multiply(multiply(X2,X2),multiply(X2,X2)))) = multiply(X2,multiply(multiply(X2,X2),multiply(multiply(X2,X2),multiply(X2,X2)))),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
multiply(multiply(X2,X2),multiply(multiply(X2,X2),multiply(X2,X2))) = identity,
inference(substitution,[status(thm)],[c87]) ).
cnf(c93,plain,
multiply(X2,multiply(multiply(X2,X2),multiply(multiply(X2,X2),multiply(X2,X2)))) = multiply(X2,identity),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
multiply(X2,multiply(multiply(X2,X2),multiply(multiply(X2,X2),multiply(X2,X2)))) = X2,
inference(transitivity,[status(thm)],[c93,c50]) ).
cnf(c95,plain,
multiply(identity,multiply(identity,multiply(multiply(X2,X2),multiply(X2,X2)))) = X2,
inference(transitivity,[status(thm)],[c91,c94]) ).
cnf(c96,plain,
multiply(identity,multiply(identity,X2)) = X2,
inference(transitivity,[status(thm)],[c80,c95]) ).
cnf(c97,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))),
inference(substitution,[status(thm)],[c96]) ).
cnf(c98,plain,
multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))) = multiply(identity,multiply(multiply(X2,X2),multiply(X2,X2))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c99,plain,
multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))) = multiply(identity,multiply(identity,multiply(multiply(X2,X2),multiply(X2,X2)))),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
multiply(identity,multiply(identity,multiply(multiply(X2,X2),multiply(X2,X2)))) = multiply(multiply(X2,X2),multiply(X2,X2)),
inference(substitution,[status(thm)],[c96]) ).
cnf(c101,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(X3,X3),multiply(X3,X3))),X2)),multiply(identity,multiply(X2,X2)))) = multiply(multiply(X3,X3),multiply(X3,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c102,plain,
multiply(multiply(X3,X3),multiply(X3,X3)) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(X3,X3),multiply(X3,X3))),X2)),multiply(identity,multiply(X2,X2)))),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
multiply(multiply(identity,multiply(multiply(X3,X3),multiply(X3,X3))),X2) = multiply(multiply(identity,X3),X2),
inference(congruence,[status(thm)],[c78]) ).
cnf(c104,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(X3,X3),multiply(X3,X3))),X2)) = multiply(identity,multiply(multiply(identity,X3),X2)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(X3,X3),multiply(X3,X3))),X2)),multiply(identity,multiply(X2,X2))) = multiply(multiply(identity,multiply(multiply(identity,X3),X2)),multiply(identity,multiply(X2,X2))),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(X3,X3),multiply(X3,X3))),X2)),multiply(identity,multiply(X2,X2)))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X3),X2)),multiply(identity,multiply(X2,X2)))),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X3),X2)),multiply(identity,multiply(X2,X2)))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c108,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(X3,X3),multiply(X3,X3))),X2)),multiply(identity,multiply(X2,X2)))) = X3,
inference(transitivity,[status(thm)],[c106,c107]) ).
cnf(c109,plain,
multiply(multiply(X2,X2),multiply(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c102,c108]) ).
cnf(c110,plain,
multiply(identity,multiply(identity,multiply(multiply(X2,X2),multiply(X2,X2)))) = X2,
inference(transitivity,[status(thm)],[c100,c109]) ).
cnf(c111,plain,
multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))) = X2,
inference(transitivity,[status(thm)],[c99,c110]) ).
cnf(c112,plain,
multiply(identity,multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = X2,
inference(transitivity,[status(thm)],[c97,c111]) ).
cnf(c113,plain,
multiply(multiply(identity,identity),X2) = X2,
inference(transitivity,[status(thm)],[c33,c112]) ).
cnf(c114,plain,
multiply(identity,X2) = X2,
inference(transitivity,[status(thm)],[c31,c113]) ).
cnf(c115,plain,
multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))) = multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))),
inference(substitution,[status(thm)],[c114]) ).
cnf(c116,plain,
multiply(X3,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))))) = multiply(X3,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
multiply(X4,multiply(X3,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(X4,multiply(X3,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))))),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))) = multiply(identity,multiply(multiply(X2,X2),multiply(X2,X2))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c119,plain,
multiply(X3,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))) = multiply(X3,multiply(identity,multiply(multiply(X2,X2),multiply(X2,X2)))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
multiply(X4,multiply(X3,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))))) = multiply(X4,multiply(X3,multiply(identity,multiply(multiply(X2,X2),multiply(X2,X2))))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
multiply(X3,multiply(identity,multiply(multiply(X2,X2),multiply(X2,X2)))) = multiply(X3,multiply(identity,X2)),
inference(congruence,[status(thm)],[c78]) ).
cnf(c122,plain,
multiply(X4,multiply(X3,multiply(identity,multiply(multiply(X2,X2),multiply(X2,X2))))) = multiply(X4,multiply(X3,multiply(identity,X2))),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
multiply(X3,multiply(identity,X2)) = multiply(X3,X2),
inference(congruence,[status(thm)],[c114]) ).
cnf(c124,plain,
multiply(X4,multiply(X3,multiply(identity,X2))) = multiply(X4,multiply(X3,X2)),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
multiply(X4,multiply(X3,multiply(identity,multiply(multiply(X2,X2),multiply(X2,X2))))) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c122,c124]) ).
cnf(c126,plain,
multiply(X4,multiply(X3,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))))) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c120,c125]) ).
cnf(c127,plain,
multiply(X4,multiply(X3,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c117,c126]) ).
cnf(c128,plain,
multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c9,c127]) ).
cnf(c129,plain,
multiply(multiply(a,b),c) = multiply(a,multiply(b,c)),
inference(substitution,[status(thm)],[c128]) ).
cnf(c130,plain,
$false,
inference(resolution,[status(thm)],[c1,c129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP118-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 09:20:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.43 Command-line arguments: --no-flatten-goal
% 0.13/0.43
% 0.13/0.43 % SZS status Unsatisfiable
% 0.13/0.43
% 0.13/0.44 % SZS output start CNFRefutation
% See solution above
% 0.50/0.51
% 0.50/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------