%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP581-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 10:11:17 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.45s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 5
% Syntax : Number of clauses : 119 ( 119 unt; 0 nHn; 8 RR)
% Number of literals : 119 ( 118 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 : 289 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(inverse(a1),a1) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
cnf(c2,axiom,
inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(c3,plain,
inverse(double_divide(X2,X)) = double_divide(double_divide(X2,X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
multiply(A2,B) = double_divide(double_divide(B,A2),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c5,plain,
multiply(X,X2) = double_divide(double_divide(X2,X),identity),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
double_divide(double_divide(X2,X),identity) = multiply(X,X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
inverse(double_divide(X2,X)) = multiply(X,X2),
inference(transitivity,[status(thm)],[c3,c6]) ).
cnf(c8,plain,
inverse(double_divide(X,inverse(X))) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(inverse(X),X) = inverse(double_divide(X,inverse(X))),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,axiom,
identity = double_divide(A2,inverse(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(c11,plain,
identity = double_divide(X,inverse(X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
double_divide(X,inverse(X)) = identity,
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
inverse(double_divide(X,inverse(X))) = inverse(identity),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(inverse(X),X) = inverse(identity),
inference(transitivity,[status(thm)],[c9,c13]) ).
cnf(c15,plain,
double_divide(X2,multiply(inverse(X),X)) = double_divide(X2,inverse(identity)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
double_divide(multiply(inverse(X3),X3),double_divide(X2,multiply(inverse(X),X))) = double_divide(multiply(inverse(X3),X3),double_divide(X2,inverse(identity))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
double_divide(identity,double_divide(multiply(inverse(X3),X3),double_divide(X2,multiply(inverse(X),X)))) = double_divide(identity,double_divide(multiply(inverse(X3),X3),double_divide(X2,inverse(identity)))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X3),X3),double_divide(X2,multiply(inverse(X),X)))),multiply(inverse(X4),X4)) = double_divide(double_divide(identity,double_divide(multiply(inverse(X3),X3),double_divide(X2,inverse(identity)))),multiply(inverse(X4),X4)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
inverse(identity) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c20,plain,
double_divide(X,inverse(identity)) = double_divide(X,double_divide(identity,identity)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
double_divide(multiply(inverse(X2),X2),double_divide(X,inverse(identity))) = double_divide(multiply(inverse(X2),X2),double_divide(X,double_divide(identity,identity))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
double_divide(identity,double_divide(multiply(inverse(X2),X2),double_divide(X,inverse(identity)))) = double_divide(identity,double_divide(multiply(inverse(X2),X2),double_divide(X,double_divide(identity,identity)))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X3),X3),double_divide(X2,inverse(identity)))),multiply(inverse(X),X)) = double_divide(double_divide(identity,double_divide(multiply(inverse(X3),X3),double_divide(X2,double_divide(identity,identity)))),multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
double_divide(multiply(inverse(X2),X2),double_divide(X,double_divide(identity,X3))) = double_divide(inverse(identity),double_divide(X,double_divide(identity,X3))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c25,plain,
double_divide(X3,double_divide(multiply(inverse(X2),X2),double_divide(X,double_divide(identity,X3)))) = double_divide(X3,double_divide(inverse(identity),double_divide(X,double_divide(identity,X3)))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
double_divide(double_divide(X4,double_divide(multiply(inverse(X3),X3),double_divide(X2,double_divide(identity,X4)))),multiply(inverse(X),X)) = double_divide(double_divide(X4,double_divide(inverse(identity),double_divide(X2,double_divide(identity,X4)))),multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
double_divide(double_divide(X3,double_divide(inverse(identity),double_divide(X2,double_divide(identity,X3)))),multiply(inverse(X),X)) = double_divide(double_divide(X3,double_divide(inverse(identity),double_divide(X2,double_divide(identity,X3)))),inverse(identity)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c28,plain,
inverse(identity) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c29,plain,
double_divide(inverse(identity),double_divide(X,double_divide(identity,X2))) = double_divide(double_divide(identity,identity),double_divide(X,double_divide(identity,X2))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
double_divide(X2,double_divide(inverse(identity),double_divide(X,double_divide(identity,X2)))) = double_divide(X2,double_divide(double_divide(identity,identity),double_divide(X,double_divide(identity,X2)))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
double_divide(double_divide(X2,double_divide(inverse(identity),double_divide(X,double_divide(identity,X2)))),inverse(identity)) = double_divide(double_divide(X2,double_divide(double_divide(identity,identity),double_divide(X,double_divide(identity,X2)))),inverse(identity)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
inverse(identity) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c33,plain,
double_divide(double_divide(X3,double_divide(double_divide(identity,X2),double_divide(X,double_divide(X2,X3)))),inverse(identity)) = double_divide(double_divide(X3,double_divide(double_divide(identity,X2),double_divide(X,double_divide(X2,X3)))),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,axiom,
double_divide(double_divide(A2,double_divide(double_divide(identity,B2),double_divide(C,double_divide(B2,A2)))),double_divide(identity,identity)) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c35,plain,
double_divide(double_divide(X3,double_divide(double_divide(identity,X2),double_divide(X,double_divide(X2,X3)))),double_divide(identity,identity)) = X,
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
double_divide(double_divide(X3,double_divide(double_divide(identity,X2),double_divide(X,double_divide(X2,X3)))),inverse(identity)) = X,
inference(transitivity,[status(thm)],[c33,c35]) ).
cnf(c37,plain,
double_divide(double_divide(X2,double_divide(double_divide(identity,identity),double_divide(X,double_divide(identity,X2)))),inverse(identity)) = X,
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
double_divide(double_divide(X2,double_divide(inverse(identity),double_divide(X,double_divide(identity,X2)))),inverse(identity)) = X,
inference(transitivity,[status(thm)],[c31,c37]) ).
cnf(c39,plain,
double_divide(double_divide(X3,double_divide(inverse(identity),double_divide(X2,double_divide(identity,X3)))),multiply(inverse(X),X)) = X2,
inference(transitivity,[status(thm)],[c27,c38]) ).
cnf(c40,plain,
double_divide(double_divide(X4,double_divide(multiply(inverse(X3),X3),double_divide(X2,double_divide(identity,X4)))),multiply(inverse(X),X)) = X2,
inference(transitivity,[status(thm)],[c26,c39]) ).
cnf(c41,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X3),X3),double_divide(X2,double_divide(identity,identity)))),multiply(inverse(X),X)) = X2,
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X3),X3),double_divide(X2,inverse(identity)))),multiply(inverse(X),X)) = X2,
inference(transitivity,[status(thm)],[c23,c41]) ).
cnf(c43,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X4),X4),double_divide(X3,multiply(inverse(X2),X2)))),multiply(inverse(X),X)) = X3,
inference(transitivity,[status(thm)],[c18,c42]) ).
cnf(c44,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X3),X3),double_divide(multiply(inverse(X4),X4),multiply(inverse(X2),X2)))),multiply(inverse(X),X)) = multiply(inverse(X4),X4),
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(inverse(X4),X4) = double_divide(double_divide(identity,double_divide(multiply(inverse(X3),X3),double_divide(multiply(inverse(X4),X4),multiply(inverse(X2),X2)))),multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
double_divide(multiply(inverse(X2),X2),multiply(inverse(X),X)) = double_divide(inverse(identity),multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c47,plain,
inverse(identity) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c48,plain,
double_divide(inverse(identity),multiply(inverse(X),X)) = double_divide(double_divide(identity,identity),multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X),X),double_divide(double_divide(multiply(inverse(X4),X4),double_divide(multiply(inverse(X3),X3),multiply(inverse(X2),X2))),multiply(inverse(X6),X6)))),multiply(inverse(X5),X5)) = double_divide(multiply(inverse(X4),X4),double_divide(multiply(inverse(X3),X3),multiply(inverse(X2),X2))),
inference(substitution,[status(thm)],[c43]) ).
cnf(c50,plain,
double_divide(multiply(inverse(X6),X6),double_divide(multiply(inverse(X5),X5),multiply(inverse(X4),X4))) = double_divide(double_divide(identity,double_divide(multiply(inverse(X3),X3),double_divide(double_divide(multiply(inverse(X6),X6),double_divide(multiply(inverse(X5),X5),multiply(inverse(X4),X4))),multiply(inverse(X2),X2)))),multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
double_divide(multiply(inverse(X2),X2),multiply(inverse(X),X)) = double_divide(multiply(inverse(X2),X2),inverse(identity)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c52,plain,
double_divide(multiply(inverse(X3),X3),double_divide(multiply(inverse(X2),X2),multiply(inverse(X),X))) = double_divide(multiply(inverse(X3),X3),double_divide(multiply(inverse(X2),X2),inverse(identity))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
double_divide(double_divide(multiply(inverse(X4),X4),double_divide(multiply(inverse(X3),X3),multiply(inverse(X2),X2))),multiply(inverse(X),X)) = double_divide(double_divide(multiply(inverse(X4),X4),double_divide(multiply(inverse(X3),X3),inverse(identity))),multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c55,plain,
double_divide(multiply(inverse(X2),X2),inverse(X)) = double_divide(multiply(inverse(X2),X2),double_divide(X,identity)),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
double_divide(multiply(inverse(X3),X3),double_divide(multiply(inverse(X2),X2),inverse(X))) = double_divide(multiply(inverse(X3),X3),double_divide(multiply(inverse(X2),X2),double_divide(X,identity))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
double_divide(double_divide(multiply(inverse(X4),X4),double_divide(multiply(inverse(X3),X3),inverse(X2))),multiply(inverse(X),X)) = double_divide(double_divide(multiply(inverse(X4),X4),double_divide(multiply(inverse(X3),X3),double_divide(X2,identity))),multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
double_divide(multiply(inverse(X3),X3),double_divide(multiply(inverse(X2),X2),double_divide(X,identity))) = double_divide(inverse(identity),double_divide(multiply(inverse(X2),X2),double_divide(X,identity))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c59,plain,
double_divide(double_divide(multiply(inverse(X4),X4),double_divide(multiply(inverse(X3),X3),double_divide(X2,identity))),multiply(inverse(X),X)) = double_divide(double_divide(inverse(identity),double_divide(multiply(inverse(X3),X3),double_divide(X2,identity))),multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
identity = double_divide(identity,inverse(identity)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c61,plain,
double_divide(X,identity) = double_divide(X,double_divide(identity,inverse(identity))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
double_divide(multiply(inverse(X2),X2),double_divide(X,identity)) = double_divide(multiply(inverse(X2),X2),double_divide(X,double_divide(identity,inverse(identity)))),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
double_divide(inverse(identity),double_divide(multiply(inverse(X2),X2),double_divide(X,identity))) = double_divide(inverse(identity),double_divide(multiply(inverse(X2),X2),double_divide(X,double_divide(identity,inverse(identity))))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
double_divide(double_divide(inverse(identity),double_divide(multiply(inverse(X3),X3),double_divide(X2,identity))),multiply(inverse(X),X)) = double_divide(double_divide(inverse(identity),double_divide(multiply(inverse(X3),X3),double_divide(X2,double_divide(identity,inverse(identity))))),multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
double_divide(double_divide(inverse(identity),double_divide(multiply(inverse(X3),X3),double_divide(X2,double_divide(identity,inverse(identity))))),multiply(inverse(X),X)) = X2,
inference(substitution,[status(thm)],[c40]) ).
cnf(c66,plain,
double_divide(double_divide(inverse(identity),double_divide(multiply(inverse(X3),X3),double_divide(X2,identity))),multiply(inverse(X),X)) = X2,
inference(transitivity,[status(thm)],[c64,c65]) ).
cnf(c67,plain,
double_divide(double_divide(multiply(inverse(X4),X4),double_divide(multiply(inverse(X3),X3),double_divide(X2,identity))),multiply(inverse(X),X)) = X2,
inference(transitivity,[status(thm)],[c59,c66]) ).
cnf(c68,plain,
double_divide(double_divide(multiply(inverse(X4),X4),double_divide(multiply(inverse(X3),X3),inverse(X2))),multiply(inverse(X),X)) = X2,
inference(transitivity,[status(thm)],[c57,c67]) ).
cnf(c69,plain,
double_divide(double_divide(multiply(inverse(X3),X3),double_divide(multiply(inverse(X2),X2),inverse(identity))),multiply(inverse(X),X)) = identity,
inference(substitution,[status(thm)],[c68]) ).
cnf(c70,plain,
double_divide(double_divide(multiply(inverse(X4),X4),double_divide(multiply(inverse(X3),X3),multiply(inverse(X2),X2))),multiply(inverse(X),X)) = identity,
inference(transitivity,[status(thm)],[c53,c69]) ).
cnf(c71,plain,
double_divide(multiply(inverse(X2),X2),double_divide(double_divide(multiply(inverse(X5),X5),double_divide(multiply(inverse(X4),X4),multiply(inverse(X3),X3))),multiply(inverse(X),X))) = double_divide(multiply(inverse(X2),X2),identity),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
double_divide(identity,double_divide(multiply(inverse(X2),X2),double_divide(double_divide(multiply(inverse(X5),X5),double_divide(multiply(inverse(X4),X4),multiply(inverse(X3),X3))),multiply(inverse(X),X)))) = double_divide(identity,double_divide(multiply(inverse(X2),X2),identity)),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X3),X3),double_divide(double_divide(multiply(inverse(X6),X6),double_divide(multiply(inverse(X5),X5),multiply(inverse(X4),X4))),multiply(inverse(X2),X2)))),multiply(inverse(X),X)) = double_divide(double_divide(identity,double_divide(multiply(inverse(X3),X3),identity)),multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
inverse(multiply(inverse(X),X)) = double_divide(multiply(inverse(X),X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c75,plain,
double_divide(multiply(inverse(X),X),identity) = inverse(multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
double_divide(identity,double_divide(multiply(inverse(X),X),identity)) = double_divide(identity,inverse(multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X2),X2),identity)),multiply(inverse(X),X)) = double_divide(double_divide(identity,inverse(multiply(inverse(X2),X2))),multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
inverse(multiply(inverse(X),X)) = double_divide(multiply(inverse(X),X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c79,plain,
double_divide(identity,inverse(multiply(inverse(X),X))) = double_divide(identity,double_divide(multiply(inverse(X),X),identity)),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
double_divide(double_divide(identity,inverse(multiply(inverse(X2),X2))),multiply(inverse(X),X)) = double_divide(double_divide(identity,double_divide(multiply(inverse(X2),X2),identity)),multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
identity = double_divide(X,inverse(X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c82,plain,
double_divide(identity,multiply(inverse(X),X)) = double_divide(double_divide(X,inverse(X)),multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
multiply(X,X2) = inverse(double_divide(X2,X)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c84,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)],[c83]) ).
cnf(c85,plain,
identity = double_divide(double_divide(X2,X),inverse(double_divide(X2,X))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c86,plain,
double_divide(double_divide(X2,X),inverse(double_divide(X2,X))) = identity,
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
double_divide(double_divide(X2,X),multiply(X,X2)) = identity,
inference(transitivity,[status(thm)],[c84,c86]) ).
cnf(c88,plain,
double_divide(double_divide(X,inverse(X)),multiply(inverse(X),X)) = identity,
inference(substitution,[status(thm)],[c87]) ).
cnf(c89,plain,
double_divide(identity,multiply(inverse(X),X)) = identity,
inference(transitivity,[status(thm)],[c82,c88]) ).
cnf(c90,plain,
identity = double_divide(identity,multiply(inverse(X),X)),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
double_divide(multiply(inverse(X2),X2),identity) = double_divide(multiply(inverse(X2),X2),double_divide(identity,multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
double_divide(identity,double_divide(multiply(inverse(X2),X2),identity)) = double_divide(identity,double_divide(multiply(inverse(X2),X2),double_divide(identity,multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X3),X3),identity)),multiply(inverse(X2),X2)) = double_divide(double_divide(identity,double_divide(multiply(inverse(X3),X3),double_divide(identity,multiply(inverse(X),X)))),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X3),X3),double_divide(identity,multiply(inverse(X),X)))),multiply(inverse(X2),X2)) = identity,
inference(substitution,[status(thm)],[c43]) ).
cnf(c95,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X2),X2),identity)),multiply(inverse(X),X)) = identity,
inference(transitivity,[status(thm)],[c93,c94]) ).
cnf(c96,plain,
double_divide(double_divide(identity,inverse(multiply(inverse(X2),X2))),multiply(inverse(X),X)) = identity,
inference(transitivity,[status(thm)],[c80,c95]) ).
cnf(c97,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X2),X2),identity)),multiply(inverse(X),X)) = identity,
inference(transitivity,[status(thm)],[c77,c96]) ).
cnf(c98,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X3),X3),double_divide(double_divide(multiply(inverse(X6),X6),double_divide(multiply(inverse(X5),X5),multiply(inverse(X4),X4))),multiply(inverse(X2),X2)))),multiply(inverse(X),X)) = identity,
inference(transitivity,[status(thm)],[c73,c97]) ).
cnf(c99,plain,
double_divide(multiply(inverse(X3),X3),double_divide(multiply(inverse(X2),X2),multiply(inverse(X),X))) = identity,
inference(transitivity,[status(thm)],[c50,c98]) ).
cnf(c100,plain,
double_divide(multiply(inverse(X2),X2),double_divide(multiply(inverse(X3),X3),multiply(inverse(X),X))) = identity,
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
identity = double_divide(multiply(inverse(X2),X2),double_divide(multiply(inverse(X3),X3),multiply(inverse(X),X))),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,plain,
double_divide(identity,identity) = double_divide(identity,double_divide(multiply(inverse(X2),X2),double_divide(multiply(inverse(X3),X3),multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
double_divide(double_divide(identity,identity),multiply(inverse(X4),X4)) = double_divide(double_divide(identity,double_divide(multiply(inverse(X2),X2),double_divide(multiply(inverse(X3),X3),multiply(inverse(X),X)))),multiply(inverse(X4),X4)),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X2),X2),double_divide(multiply(inverse(X3),X3),multiply(inverse(X),X)))),multiply(inverse(X4),X4)) = multiply(inverse(X3),X3),
inference(substitution,[status(thm)],[c43]) ).
cnf(c105,plain,
double_divide(double_divide(identity,identity),multiply(inverse(X2),X2)) = multiply(inverse(X),X),
inference(transitivity,[status(thm)],[c103,c104]) ).
cnf(c106,plain,
double_divide(inverse(identity),multiply(inverse(X2),X2)) = multiply(inverse(X),X),
inference(transitivity,[status(thm)],[c48,c105]) ).
cnf(c107,plain,
double_divide(multiply(inverse(X3),X3),multiply(inverse(X2),X2)) = multiply(inverse(X),X),
inference(transitivity,[status(thm)],[c46,c106]) ).
cnf(c108,plain,
double_divide(multiply(inverse(X3),X3),double_divide(multiply(inverse(X4),X4),multiply(inverse(X2),X2))) = double_divide(multiply(inverse(X3),X3),multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
double_divide(identity,double_divide(multiply(inverse(X3),X3),double_divide(multiply(inverse(X4),X4),multiply(inverse(X2),X2)))) = double_divide(identity,double_divide(multiply(inverse(X3),X3),multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X4),X4),double_divide(multiply(inverse(X5),X5),multiply(inverse(X3),X3)))),multiply(inverse(X2),X2)) = double_divide(double_divide(identity,double_divide(multiply(inverse(X4),X4),multiply(inverse(X),X))),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
double_divide(identity,double_divide(multiply(inverse(X3),X3),multiply(inverse(X2),X2))) = double_divide(identity,multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c107]) ).
cnf(c112,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X4),X4),multiply(inverse(X2),X2))),multiply(inverse(X3),X3)) = double_divide(double_divide(identity,multiply(inverse(X),X)),multiply(inverse(X3),X3)),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
double_divide(double_divide(identity,multiply(inverse(X),X)),multiply(inverse(X2),X2)) = double_divide(identity,multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c89]) ).
cnf(c114,plain,
double_divide(double_divide(identity,multiply(inverse(X),X)),multiply(inverse(X2),X2)) = identity,
inference(transitivity,[status(thm)],[c113,c89]) ).
cnf(c115,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X3),X3),multiply(inverse(X),X))),multiply(inverse(X2),X2)) = identity,
inference(transitivity,[status(thm)],[c112,c114]) ).
cnf(c116,plain,
double_divide(double_divide(identity,double_divide(multiply(inverse(X3),X3),double_divide(multiply(inverse(X4),X4),multiply(inverse(X2),X2)))),multiply(inverse(X),X)) = identity,
inference(transitivity,[status(thm)],[c110,c115]) ).
cnf(c117,plain,
multiply(inverse(X),X) = identity,
inference(transitivity,[status(thm)],[c45,c116]) ).
cnf(c118,plain,
multiply(inverse(a1),a1) = identity,
inference(substitution,[status(thm)],[c117]) ).
cnf(c119,plain,
$false,
inference(resolution,[status(thm)],[c1,c118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP581-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:07:44 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.45 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
% 0.11/0.45
% 0.11/0.45 % SZS status Unsatisfiable
% 0.11/0.45
% 0.18/0.48 % SZS output start CNFRefutation
% See solution above
% 0.18/0.54
% 0.18/0.54 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------