%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP487-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 10:10:48 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : CNFRefutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 5
% Syntax : Number of clauses : 146 ( 146 unt; 0 nHn; 5 RR)
% Number of literals : 146 ( 145 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 251 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(inverse(a1),a1) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
cnf(c2,axiom,
inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
cnf(c3,plain,
inverse(inverse(X)) = double_divide(inverse(X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
double_divide(identity,inverse(inverse(X))) = double_divide(identity,double_divide(inverse(X),identity)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(X2,double_divide(identity,inverse(inverse(X)))) = multiply(X2,double_divide(identity,double_divide(inverse(X),identity))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
double_divide(X2,multiply(X,double_divide(identity,inverse(inverse(X2))))) = double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),identity)))),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
identity = double_divide(A2,inverse(A2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
cnf(c8,plain,
identity = double_divide(X,inverse(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
double_divide(inverse(X2),identity) = double_divide(inverse(X2),double_divide(X,inverse(X))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
double_divide(identity,double_divide(inverse(X2),identity)) = double_divide(identity,double_divide(inverse(X2),double_divide(X,inverse(X)))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(X,double_divide(identity,double_divide(inverse(X2),identity))) = multiply(X,double_divide(identity,double_divide(inverse(X2),double_divide(X,inverse(X))))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),identity)))) = double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),double_divide(X,inverse(X)))))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
double_divide(inverse(X2),double_divide(X,X3)) = double_divide(double_divide(X2,identity),double_divide(X,X3)),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
double_divide(identity,double_divide(inverse(X3),double_divide(X2,X))) = double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(X2,double_divide(identity,double_divide(inverse(X3),double_divide(X2,X)))) = multiply(X2,double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X)))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
double_divide(X3,multiply(X2,double_divide(identity,double_divide(inverse(X3),double_divide(X2,X))))) = double_divide(X3,multiply(X2,double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
inverse(double_divide(X2,X)) = double_divide(double_divide(X2,X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c19,axiom,
multiply(A2,B) = double_divide(double_divide(B,A2),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(c20,plain,
multiply(X,X2) = double_divide(double_divide(X2,X),identity),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
double_divide(double_divide(X2,X),identity) = multiply(X,X2),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
inverse(double_divide(X2,X)) = multiply(X,X2),
inference(transitivity,[status(thm)],[c18,c21]) ).
cnf(c23,plain,
inverse(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),X2)) = multiply(X2,double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X)))),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(X2,double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X)))) = inverse(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),X2)),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
double_divide(X3,multiply(X2,double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))))) = double_divide(X3,inverse(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),X2))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
inverse(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),X2)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),X2),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c27,plain,
double_divide(X3,inverse(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),X2))) = double_divide(X3,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),X2),identity)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,axiom,
double_divide(A2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A2,identity),double_divide(B2,C))),B2),identity)) = C,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(c29,plain,
double_divide(X3,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),X2),identity)) = X,
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
double_divide(X3,inverse(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),X2))) = X,
inference(transitivity,[status(thm)],[c27,c29]) ).
cnf(c31,plain,
double_divide(X3,multiply(X2,double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))))) = X,
inference(transitivity,[status(thm)],[c25,c30]) ).
cnf(c32,plain,
double_divide(X3,multiply(X2,double_divide(identity,double_divide(inverse(X3),double_divide(X2,X))))) = X,
inference(transitivity,[status(thm)],[c17,c31]) ).
cnf(c33,plain,
double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),double_divide(X,inverse(X)))))) = inverse(X),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),identity)))) = inverse(X),
inference(transitivity,[status(thm)],[c12,c33]) ).
cnf(c35,plain,
double_divide(X2,multiply(X,double_divide(identity,inverse(inverse(X2))))) = inverse(X),
inference(transitivity,[status(thm)],[c6,c34]) ).
cnf(c36,plain,
double_divide(X,multiply(multiply(inverse(X2),X2),double_divide(identity,inverse(inverse(X))))) = inverse(multiply(inverse(X2),X2)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
inverse(multiply(inverse(X2),X2)) = double_divide(X,multiply(multiply(inverse(X2),X2),double_divide(identity,inverse(inverse(X))))),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
inverse(inverse(X)) = double_divide(inverse(X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c39,plain,
double_divide(identity,inverse(inverse(X))) = double_divide(identity,double_divide(inverse(X),identity)),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
multiply(multiply(inverse(X2),X2),double_divide(identity,inverse(inverse(X)))) = multiply(multiply(inverse(X2),X2),double_divide(identity,double_divide(inverse(X),identity))),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
double_divide(X,multiply(multiply(inverse(X2),X2),double_divide(identity,inverse(inverse(X))))) = double_divide(X,multiply(multiply(inverse(X2),X2),double_divide(identity,double_divide(inverse(X),identity)))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
inverse(double_divide(X,inverse(X))) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c43,plain,
multiply(inverse(X),X) = inverse(double_divide(X,inverse(X))),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
identity = double_divide(X,inverse(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c45,plain,
double_divide(X,inverse(X)) = identity,
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
inverse(double_divide(X,inverse(X))) = inverse(identity),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
multiply(inverse(X),X) = inverse(identity),
inference(transitivity,[status(thm)],[c43,c46]) ).
cnf(c48,plain,
identity = double_divide(X,inverse(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c49,plain,
inverse(identity) = inverse(double_divide(X,inverse(X))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
inverse(double_divide(X,inverse(X))) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c51,plain,
inverse(identity) = multiply(inverse(X),X),
inference(transitivity,[status(thm)],[c49,c50]) ).
cnf(c52,plain,
multiply(inverse(X),X) = multiply(inverse(X2),X2),
inference(transitivity,[status(thm)],[c47,c51]) ).
cnf(c53,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
double_divide(multiply(inverse(X2),X2),multiply(inverse(X),X)) = double_divide(multiply(inverse(X2),X2),multiply(inverse(multiply(inverse(X2),X2)),multiply(inverse(X2),X2))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(inverse(X2),multiply(inverse(X),X)) = multiply(inverse(X2),inverse(identity)),
inference(congruence,[status(thm)],[c47]) ).
cnf(c56,plain,
double_divide(X2,multiply(inverse(X2),multiply(inverse(X),X))) = double_divide(X2,multiply(inverse(X2),inverse(identity))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
inverse(identity) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c58,plain,
multiply(inverse(X),inverse(identity)) = multiply(inverse(X),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
double_divide(X,multiply(inverse(X),inverse(identity))) = double_divide(X,multiply(inverse(X),double_divide(identity,identity))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
identity = double_divide(inverse(X),inverse(inverse(X))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c61,plain,
double_divide(identity,identity) = double_divide(identity,double_divide(inverse(X),inverse(inverse(X)))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
multiply(inverse(X),double_divide(identity,identity)) = multiply(inverse(X),double_divide(identity,double_divide(inverse(X),inverse(inverse(X))))),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
double_divide(X,multiply(inverse(X),double_divide(identity,identity))) = double_divide(X,multiply(inverse(X),double_divide(identity,double_divide(inverse(X),inverse(inverse(X)))))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c65,plain,
double_divide(inverse(X2),inverse(X)) = double_divide(inverse(X2),double_divide(X,identity)),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
double_divide(identity,double_divide(inverse(X2),inverse(X))) = double_divide(identity,double_divide(inverse(X2),double_divide(X,identity))),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
multiply(X,double_divide(identity,double_divide(inverse(X2),inverse(X)))) = multiply(X,double_divide(identity,double_divide(inverse(X2),double_divide(X,identity)))),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),inverse(X))))) = double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),double_divide(X,identity))))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),double_divide(X,identity))))) = identity,
inference(substitution,[status(thm)],[c32]) ).
cnf(c70,plain,
double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),inverse(X))))) = identity,
inference(transitivity,[status(thm)],[c68,c69]) ).
cnf(c71,plain,
double_divide(X,multiply(inverse(X),double_divide(identity,double_divide(inverse(X),inverse(inverse(X)))))) = identity,
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,plain,
double_divide(X,multiply(inverse(X),double_divide(identity,identity))) = identity,
inference(transitivity,[status(thm)],[c63,c71]) ).
cnf(c73,plain,
double_divide(X,multiply(inverse(X),inverse(identity))) = identity,
inference(transitivity,[status(thm)],[c59,c72]) ).
cnf(c74,plain,
double_divide(X2,multiply(inverse(X2),multiply(inverse(X),X))) = identity,
inference(transitivity,[status(thm)],[c56,c73]) ).
cnf(c75,plain,
double_divide(multiply(inverse(X),X),multiply(inverse(multiply(inverse(X),X)),multiply(inverse(X),X))) = identity,
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
double_divide(multiply(inverse(X2),X2),multiply(inverse(X),X)) = identity,
inference(transitivity,[status(thm)],[c54,c75]) ).
cnf(c77,plain,
identity = double_divide(multiply(inverse(X2),X2),multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
double_divide(inverse(X),identity) = double_divide(inverse(X),double_divide(multiply(inverse(X3),X3),multiply(inverse(X2),X2))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
double_divide(identity,double_divide(inverse(X),identity)) = double_divide(identity,double_divide(inverse(X),double_divide(multiply(inverse(X3),X3),multiply(inverse(X2),X2)))),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
multiply(multiply(inverse(X3),X3),double_divide(identity,double_divide(inverse(X),identity))) = multiply(multiply(inverse(X3),X3),double_divide(identity,double_divide(inverse(X),double_divide(multiply(inverse(X3),X3),multiply(inverse(X2),X2))))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
double_divide(X,multiply(multiply(inverse(X3),X3),double_divide(identity,double_divide(inverse(X),identity)))) = double_divide(X,multiply(multiply(inverse(X3),X3),double_divide(identity,double_divide(inverse(X),double_divide(multiply(inverse(X3),X3),multiply(inverse(X2),X2)))))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
double_divide(X,multiply(multiply(inverse(X3),X3),double_divide(identity,double_divide(inverse(X),double_divide(multiply(inverse(X3),X3),multiply(inverse(X2),X2)))))) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c32]) ).
cnf(c83,plain,
double_divide(X,multiply(multiply(inverse(X3),X3),double_divide(identity,double_divide(inverse(X),identity)))) = multiply(inverse(X2),X2),
inference(transitivity,[status(thm)],[c81,c82]) ).
cnf(c84,plain,
double_divide(X,multiply(multiply(inverse(X3),X3),double_divide(identity,inverse(inverse(X))))) = multiply(inverse(X2),X2),
inference(transitivity,[status(thm)],[c41,c83]) ).
cnf(c85,plain,
inverse(multiply(inverse(X2),X2)) = multiply(inverse(X),X),
inference(transitivity,[status(thm)],[c37,c84]) ).
cnf(c86,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
inverse(multiply(inverse(X),X)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c85]) ).
cnf(c89,plain,
multiply(inverse(X2),X2) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
inverse(multiply(inverse(X2),X2)) = inverse(inverse(multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
inverse(double_divide(X,identity)) = multiply(identity,X),
inference(substitution,[status(thm)],[c22]) ).
cnf(c92,plain,
multiply(identity,X) = inverse(double_divide(X,identity)),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c94,plain,
double_divide(X,identity) = inverse(X),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
inverse(double_divide(X,identity)) = inverse(inverse(X)),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
multiply(identity,X) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c92,c95]) ).
cnf(c97,plain,
multiply(identity,multiply(inverse(X),X)) = inverse(inverse(multiply(inverse(X),X))),
inference(substitution,[status(thm)],[c96]) ).
cnf(c98,plain,
inverse(inverse(multiply(inverse(X),X))) = multiply(identity,multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,plain,
inverse(multiply(inverse(X),X)) = inverse(inverse(identity)),
inference(congruence,[status(thm)],[c47]) ).
cnf(c100,plain,
multiply(inverse(multiply(inverse(X),X)),identity) = multiply(inverse(inverse(identity)),identity),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),identity)) = inverse(multiply(inverse(inverse(identity)),identity)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
multiply(inverse(X),X) = multiply(inverse(double_divide(identity,inverse(inverse(X2)))),double_divide(identity,inverse(inverse(X2)))),
inference(substitution,[status(thm)],[c52]) ).
cnf(c103,plain,
double_divide(X2,multiply(inverse(X),X)) = double_divide(X2,multiply(inverse(double_divide(identity,inverse(inverse(X2)))),double_divide(identity,inverse(inverse(X2))))),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
double_divide(X,multiply(inverse(double_divide(identity,inverse(inverse(X)))),double_divide(identity,inverse(inverse(X))))) = inverse(inverse(double_divide(identity,inverse(inverse(X))))),
inference(substitution,[status(thm)],[c35]) ).
cnf(c105,plain,
inverse(double_divide(identity,inverse(inverse(X)))) = multiply(inverse(inverse(X)),identity),
inference(substitution,[status(thm)],[c22]) ).
cnf(c106,plain,
inverse(inverse(double_divide(identity,inverse(inverse(X))))) = inverse(multiply(inverse(inverse(X)),identity)),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
double_divide(X,multiply(inverse(double_divide(identity,inverse(inverse(X)))),double_divide(identity,inverse(inverse(X))))) = inverse(multiply(inverse(inverse(X)),identity)),
inference(transitivity,[status(thm)],[c104,c106]) ).
cnf(c108,plain,
double_divide(X2,multiply(inverse(X),X)) = inverse(multiply(inverse(inverse(X2)),identity)),
inference(transitivity,[status(thm)],[c103,c107]) ).
cnf(c109,plain,
double_divide(identity,multiply(inverse(X),X)) = inverse(multiply(inverse(inverse(identity)),identity)),
inference(substitution,[status(thm)],[c108]) ).
cnf(c110,plain,
inverse(multiply(inverse(inverse(identity)),identity)) = double_divide(identity,multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
identity = double_divide(X,inverse(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c112,plain,
double_divide(identity,multiply(inverse(X),X)) = double_divide(double_divide(X,inverse(X)),multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
multiply(X,X2) = inverse(double_divide(X2,X)),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c114,plain,
double_divide(double_divide(X2,X),multiply(X,X2)) = double_divide(double_divide(X2,X),inverse(double_divide(X2,X))),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
identity = double_divide(double_divide(X2,X),inverse(double_divide(X2,X))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c116,plain,
double_divide(double_divide(X2,X),inverse(double_divide(X2,X))) = identity,
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
double_divide(double_divide(X2,X),multiply(X,X2)) = identity,
inference(transitivity,[status(thm)],[c114,c116]) ).
cnf(c118,plain,
double_divide(double_divide(X,inverse(X)),multiply(inverse(X),X)) = identity,
inference(substitution,[status(thm)],[c117]) ).
cnf(c119,plain,
double_divide(identity,multiply(inverse(X),X)) = identity,
inference(transitivity,[status(thm)],[c112,c118]) ).
cnf(c120,plain,
inverse(multiply(inverse(inverse(identity)),identity)) = identity,
inference(transitivity,[status(thm)],[c110,c119]) ).
cnf(c121,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),identity)) = identity,
inference(transitivity,[status(thm)],[c101,c120]) ).
cnf(c122,plain,
identity = inverse(multiply(inverse(multiply(inverse(X),X)),identity)),
inference(symmetry,[status(thm)],[c121]) ).
cnf(c123,plain,
multiply(identity,multiply(inverse(X2),X2)) = multiply(inverse(multiply(inverse(multiply(inverse(X),X)),identity)),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
double_divide(X,multiply(X3,double_divide(identity,double_divide(inverse(X),double_divide(X3,multiply(inverse(X3),multiply(inverse(X2),X2))))))) = multiply(inverse(X3),multiply(inverse(X2),X2)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c125,plain,
multiply(inverse(X3),multiply(inverse(X2),X2)) = double_divide(X,multiply(X3,double_divide(identity,double_divide(inverse(X),double_divide(X3,multiply(inverse(X3),multiply(inverse(X2),X2))))))),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
double_divide(inverse(X),double_divide(X3,multiply(inverse(X3),multiply(inverse(X2),X2)))) = double_divide(inverse(X),identity),
inference(congruence,[status(thm)],[c74]) ).
cnf(c127,plain,
double_divide(identity,double_divide(inverse(X),double_divide(X3,multiply(inverse(X3),multiply(inverse(X2),X2))))) = double_divide(identity,double_divide(inverse(X),identity)),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
multiply(X3,double_divide(identity,double_divide(inverse(X),double_divide(X3,multiply(inverse(X3),multiply(inverse(X2),X2)))))) = multiply(X3,double_divide(identity,double_divide(inverse(X),identity))),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
double_divide(X,multiply(X3,double_divide(identity,double_divide(inverse(X),double_divide(X3,multiply(inverse(X3),multiply(inverse(X2),X2))))))) = double_divide(X,multiply(X3,double_divide(identity,double_divide(inverse(X),identity)))),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
inverse(inverse(X)) = double_divide(inverse(X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c131,plain,
double_divide(inverse(X),identity) = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
double_divide(identity,double_divide(inverse(X),identity)) = double_divide(identity,inverse(inverse(X))),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
multiply(X2,double_divide(identity,double_divide(inverse(X),identity))) = multiply(X2,double_divide(identity,inverse(inverse(X)))),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
double_divide(X,multiply(X2,double_divide(identity,double_divide(inverse(X),identity)))) = double_divide(X,multiply(X2,double_divide(identity,inverse(inverse(X))))),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
double_divide(X,multiply(X2,double_divide(identity,inverse(inverse(X))))) = inverse(X2),
inference(substitution,[status(thm)],[c35]) ).
cnf(c136,plain,
double_divide(X,multiply(X2,double_divide(identity,double_divide(inverse(X),identity)))) = inverse(X2),
inference(transitivity,[status(thm)],[c134,c135]) ).
cnf(c137,plain,
double_divide(X,multiply(X3,double_divide(identity,double_divide(inverse(X),double_divide(X3,multiply(inverse(X3),multiply(inverse(X2),X2))))))) = inverse(X3),
inference(transitivity,[status(thm)],[c129,c136]) ).
cnf(c138,plain,
multiply(inverse(X2),multiply(inverse(X),X)) = inverse(X2),
inference(transitivity,[status(thm)],[c125,c137]) ).
cnf(c139,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X),X)),identity)),multiply(inverse(X2),X2)) = inverse(multiply(inverse(multiply(inverse(X),X)),identity)),
inference(substitution,[status(thm)],[c138]) ).
cnf(c140,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X),X)),identity)),multiply(inverse(X2),X2)) = identity,
inference(transitivity,[status(thm)],[c139,c121]) ).
cnf(c141,plain,
multiply(identity,multiply(inverse(X),X)) = identity,
inference(transitivity,[status(thm)],[c123,c140]) ).
cnf(c142,plain,
inverse(inverse(multiply(inverse(X),X))) = identity,
inference(transitivity,[status(thm)],[c98,c141]) ).
cnf(c143,plain,
inverse(multiply(inverse(X),X)) = identity,
inference(transitivity,[status(thm)],[c90,c142]) ).
cnf(c144,plain,
multiply(inverse(X),X) = identity,
inference(transitivity,[status(thm)],[c87,c143]) ).
cnf(c145,plain,
multiply(inverse(a1),a1) = identity,
inference(substitution,[status(thm)],[c144]) ).
cnf(c146,plain,
$false,
inference(resolution,[status(thm)],[c1,c145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP487-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 10:09:16 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.44 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.10/0.44
% 0.10/0.44 % SZS status Unsatisfiable
% 0.10/0.44
% 0.10/0.45 % SZS output start CNFRefutation
% See solution above
% 0.35/0.49
% 0.35/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------