%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP576-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 10:11:16 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 5
% Syntax : Number of clauses : 182 ( 182 unt; 0 nHn; 27 RR)
% Number of literals : 182 ( 181 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 240 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_4) ).
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,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
inverse(identity) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c11,plain,
double_divide(double_divide(X2,double_divide(double_divide(X,double_divide(X3,X2)),inverse(X3))),inverse(identity)) = double_divide(double_divide(X2,double_divide(double_divide(X,double_divide(X3,X2)),inverse(X3))),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
double_divide(double_divide(X2,double_divide(X,X3)),inverse(X)) = double_divide(double_divide(X2,double_divide(X,X3)),double_divide(X,identity)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
double_divide(X3,double_divide(double_divide(X2,double_divide(X,X3)),inverse(X))) = double_divide(X3,double_divide(double_divide(X2,double_divide(X,X3)),double_divide(X,identity))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
double_divide(double_divide(X3,double_divide(double_divide(X2,double_divide(X,X3)),inverse(X))),double_divide(identity,identity)) = double_divide(double_divide(X3,double_divide(double_divide(X2,double_divide(X,X3)),double_divide(X,identity))),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,axiom,
double_divide(double_divide(A2,double_divide(double_divide(B2,double_divide(C,A2)),double_divide(C,identity))),double_divide(identity,identity)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c17,plain,
double_divide(double_divide(X3,double_divide(double_divide(X2,double_divide(X,X3)),double_divide(X,identity))),double_divide(identity,identity)) = X2,
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
double_divide(double_divide(X3,double_divide(double_divide(X2,double_divide(X,X3)),inverse(X))),double_divide(identity,identity)) = X2,
inference(transitivity,[status(thm)],[c15,c17]) ).
cnf(c19,plain,
double_divide(double_divide(X3,double_divide(double_divide(X2,double_divide(X,X3)),inverse(X))),inverse(identity)) = X2,
inference(transitivity,[status(thm)],[c11,c18]) ).
cnf(c20,plain,
double_divide(double_divide(X2,double_divide(double_divide(inverse(double_divide(X,X2)),double_divide(X,X2)),inverse(X))),inverse(identity)) = inverse(double_divide(X,X2)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
inverse(double_divide(X,X2)) = double_divide(double_divide(X2,double_divide(double_divide(inverse(double_divide(X,X2)),double_divide(X,X2)),inverse(X))),inverse(identity)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
inverse(double_divide(X,identity)) = multiply(identity,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c23,plain,
multiply(identity,X) = inverse(double_divide(X,identity)),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c25,plain,
double_divide(X,identity) = inverse(X),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
inverse(double_divide(X,identity)) = inverse(inverse(X)),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(identity,X) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c23,c26]) ).
cnf(c28,plain,
inverse(inverse(X)) = multiply(identity,X),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
inverse(inverse(inverse(X))) = double_divide(inverse(inverse(X)),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c30,plain,
double_divide(inverse(inverse(inverse(X))),inverse(identity)) = double_divide(double_divide(inverse(inverse(X)),identity),inverse(identity)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,axiom,
identity = double_divide(A2,inverse(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(c32,plain,
identity = double_divide(inverse(X),inverse(inverse(X))),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
double_divide(inverse(inverse(X)),identity) = double_divide(inverse(inverse(X)),double_divide(inverse(X),inverse(inverse(X)))),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
double_divide(double_divide(inverse(inverse(X)),identity),inverse(identity)) = double_divide(double_divide(inverse(inverse(X)),double_divide(inverse(X),inverse(inverse(X)))),inverse(identity)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c36,plain,
double_divide(inverse(X),inverse(X2)) = double_divide(double_divide(X,identity),inverse(X2)),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
double_divide(inverse(X2),double_divide(inverse(X),inverse(X2))) = double_divide(inverse(X2),double_divide(double_divide(X,identity),inverse(X2))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
double_divide(double_divide(inverse(X2),double_divide(inverse(X),inverse(X2))),inverse(identity)) = double_divide(double_divide(inverse(X2),double_divide(double_divide(X,identity),inverse(X2))),inverse(identity)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
identity = double_divide(X,inverse(X)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c40,plain,
double_divide(X,identity) = double_divide(X,double_divide(X2,inverse(X2))),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
double_divide(double_divide(X,identity),inverse(X2)) = double_divide(double_divide(X,double_divide(X2,inverse(X2))),inverse(X2)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
double_divide(inverse(X2),double_divide(double_divide(X,identity),inverse(X2))) = double_divide(inverse(X2),double_divide(double_divide(X,double_divide(X2,inverse(X2))),inverse(X2))),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
double_divide(double_divide(inverse(X2),double_divide(double_divide(X,identity),inverse(X2))),inverse(identity)) = double_divide(double_divide(inverse(X2),double_divide(double_divide(X,double_divide(X2,inverse(X2))),inverse(X2))),inverse(identity)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
double_divide(double_divide(inverse(X2),double_divide(double_divide(X,double_divide(X2,inverse(X2))),inverse(X2))),inverse(identity)) = X,
inference(substitution,[status(thm)],[c19]) ).
cnf(c45,plain,
double_divide(double_divide(inverse(X2),double_divide(double_divide(X,identity),inverse(X2))),inverse(identity)) = X,
inference(transitivity,[status(thm)],[c43,c44]) ).
cnf(c46,plain,
double_divide(double_divide(inverse(X2),double_divide(inverse(X),inverse(X2))),inverse(identity)) = X,
inference(transitivity,[status(thm)],[c38,c45]) ).
cnf(c47,plain,
double_divide(double_divide(inverse(inverse(X)),double_divide(inverse(X),inverse(inverse(X)))),inverse(identity)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
double_divide(double_divide(inverse(inverse(X)),identity),inverse(identity)) = X,
inference(transitivity,[status(thm)],[c34,c47]) ).
cnf(c49,plain,
double_divide(inverse(inverse(inverse(X))),inverse(identity)) = X,
inference(transitivity,[status(thm)],[c30,c48]) ).
cnf(c50,plain,
double_divide(inverse(inverse(inverse(inverse(identity)))),inverse(identity)) = inverse(identity),
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
inverse(identity) = double_divide(inverse(inverse(inverse(inverse(identity)))),inverse(identity)),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
X = double_divide(inverse(inverse(inverse(X))),inverse(identity)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c53,plain,
double_divide(inverse(identity),X) = double_divide(inverse(identity),double_divide(inverse(inverse(inverse(X))),inverse(identity))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
double_divide(double_divide(inverse(identity),X),inverse(identity)) = double_divide(double_divide(inverse(identity),double_divide(inverse(inverse(inverse(X))),inverse(identity))),inverse(identity)),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
double_divide(double_divide(inverse(identity),double_divide(inverse(inverse(inverse(X))),inverse(identity))),inverse(identity)) = inverse(inverse(X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c56,plain,
double_divide(double_divide(inverse(identity),X),inverse(identity)) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c54,c55]) ).
cnf(c57,plain,
double_divide(double_divide(inverse(identity),inverse(inverse(identity))),inverse(identity)) = inverse(inverse(inverse(inverse(identity)))),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
inverse(inverse(inverse(inverse(identity)))) = double_divide(double_divide(inverse(identity),inverse(inverse(identity))),inverse(identity)),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
identity = double_divide(inverse(identity),inverse(inverse(identity))),
inference(substitution,[status(thm)],[c31]) ).
cnf(c60,plain,
double_divide(inverse(identity),inverse(inverse(identity))) = identity,
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
double_divide(double_divide(inverse(identity),inverse(inverse(identity))),inverse(identity)) = double_divide(identity,inverse(identity)),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
identity = double_divide(identity,inverse(identity)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c63,plain,
double_divide(identity,inverse(identity)) = identity,
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
double_divide(double_divide(inverse(identity),inverse(inverse(identity))),inverse(identity)) = identity,
inference(transitivity,[status(thm)],[c61,c63]) ).
cnf(c65,plain,
inverse(inverse(inverse(inverse(identity)))) = identity,
inference(transitivity,[status(thm)],[c58,c64]) ).
cnf(c66,plain,
double_divide(inverse(inverse(inverse(inverse(identity)))),inverse(identity)) = double_divide(identity,inverse(identity)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
identity = double_divide(identity,inverse(identity)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c68,plain,
double_divide(identity,inverse(identity)) = identity,
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
double_divide(inverse(inverse(inverse(inverse(identity)))),inverse(identity)) = identity,
inference(transitivity,[status(thm)],[c66,c68]) ).
cnf(c70,plain,
inverse(identity) = identity,
inference(transitivity,[status(thm)],[c51,c69]) ).
cnf(c71,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
multiply(identity,X) = multiply(inverse(identity),X),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
inverse(double_divide(X,inverse(X))) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c74,plain,
multiply(inverse(X),X) = inverse(double_divide(X,inverse(X))),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
identity = double_divide(X,inverse(X)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c76,plain,
double_divide(X,inverse(X)) = identity,
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
inverse(double_divide(X,inverse(X))) = inverse(identity),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
multiply(inverse(X),X) = inverse(identity),
inference(transitivity,[status(thm)],[c74,c77]) ).
cnf(c79,plain,
inverse(identity) = multiply(inverse(X),X),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
multiply(inverse(identity),X) = multiply(multiply(inverse(X),X),X),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
inverse(double_divide(X2,multiply(inverse(X2),X))) = multiply(multiply(inverse(X2),X),X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c82,plain,
multiply(multiply(inverse(X2),X),X2) = inverse(double_divide(X2,multiply(inverse(X2),X))),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
inverse(double_divide(X2,multiply(inverse(X2),X))) = double_divide(double_divide(X2,multiply(inverse(X2),X)),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c84,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c85,plain,
double_divide(double_divide(X2,multiply(inverse(X2),X)),identity) = double_divide(double_divide(X2,multiply(inverse(X2),X)),inverse(identity)),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c87,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
inverse(multiply(X2,X)) = inverse(inverse(double_divide(X,X2))),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
inverse(inverse(multiply(X2,X))) = inverse(inverse(inverse(double_divide(X,X2)))),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
inverse(inverse(inverse(multiply(X2,X)))) = inverse(inverse(inverse(inverse(double_divide(X,X2))))),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
multiply(identity,inverse(X)) = inverse(inverse(inverse(X))),
inference(substitution,[status(thm)],[c27]) ).
cnf(c92,plain,
inverse(inverse(inverse(X))) = multiply(identity,inverse(X)),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
inverse(inverse(inverse(inverse(X)))) = inverse(multiply(identity,inverse(X))),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c95,plain,
multiply(identity,inverse(X)) = multiply(inverse(identity),inverse(X)),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
inverse(multiply(identity,inverse(X))) = inverse(multiply(inverse(identity),inverse(X))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
inverse(double_divide(inverse(X),inverse(identity))) = multiply(inverse(identity),inverse(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c98,plain,
multiply(inverse(identity),inverse(X)) = inverse(double_divide(inverse(X),inverse(identity))),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,plain,
inverse(multiply(inverse(identity),inverse(X))) = inverse(inverse(double_divide(inverse(X),inverse(identity)))),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
double_divide(double_divide(inverse(identity),double_divide(inverse(X),inverse(identity))),inverse(identity)) = inverse(inverse(double_divide(inverse(X),inverse(identity)))),
inference(substitution,[status(thm)],[c56]) ).
cnf(c101,plain,
inverse(inverse(double_divide(inverse(X),inverse(identity)))) = double_divide(double_divide(inverse(identity),double_divide(inverse(X),inverse(identity))),inverse(identity)),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,plain,
double_divide(double_divide(inverse(identity),double_divide(inverse(X),inverse(identity))),inverse(identity)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c103,plain,
inverse(inverse(double_divide(inverse(X),inverse(identity)))) = X,
inference(transitivity,[status(thm)],[c101,c102]) ).
cnf(c104,plain,
inverse(multiply(inverse(identity),inverse(X))) = X,
inference(transitivity,[status(thm)],[c99,c103]) ).
cnf(c105,plain,
inverse(multiply(identity,inverse(X))) = X,
inference(transitivity,[status(thm)],[c96,c104]) ).
cnf(c106,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference(transitivity,[status(thm)],[c93,c105]) ).
cnf(c107,plain,
inverse(inverse(inverse(inverse(double_divide(X,X2))))) = double_divide(X,X2),
inference(substitution,[status(thm)],[c106]) ).
cnf(c108,plain,
inverse(inverse(inverse(multiply(X2,X)))) = double_divide(X,X2),
inference(transitivity,[status(thm)],[c90,c107]) ).
cnf(c109,plain,
inverse(inverse(inverse(multiply(X,identity)))) = double_divide(identity,X),
inference(substitution,[status(thm)],[c108]) ).
cnf(c110,plain,
double_divide(identity,X) = inverse(inverse(inverse(multiply(X,identity)))),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
inverse(double_divide(identity,X)) = multiply(X,identity),
inference(substitution,[status(thm)],[c7]) ).
cnf(c112,plain,
multiply(X,identity) = inverse(double_divide(identity,X)),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
inverse(double_divide(identity,X)) = double_divide(double_divide(identity,X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c114,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c115,plain,
double_divide(double_divide(identity,X),identity) = double_divide(double_divide(identity,X),inverse(identity)),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c117,plain,
double_divide(identity,X) = double_divide(inverse(identity),X),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
double_divide(double_divide(identity,X),inverse(identity)) = double_divide(double_divide(inverse(identity),X),inverse(identity)),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
double_divide(double_divide(identity,X),inverse(identity)) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c118,c56]) ).
cnf(c120,plain,
double_divide(double_divide(identity,X),identity) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c115,c119]) ).
cnf(c121,plain,
inverse(double_divide(identity,X)) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c113,c120]) ).
cnf(c122,plain,
multiply(X,identity) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c112,c121]) ).
cnf(c123,plain,
inverse(multiply(X,identity)) = inverse(inverse(inverse(X))),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
inverse(inverse(multiply(X,identity))) = inverse(inverse(inverse(inverse(X)))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
inverse(inverse(inverse(multiply(X,identity)))) = inverse(inverse(inverse(inverse(inverse(X))))),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
inverse(inverse(inverse(inverse(inverse(X))))) = inverse(X),
inference(substitution,[status(thm)],[c106]) ).
cnf(c127,plain,
inverse(inverse(inverse(multiply(X,identity)))) = inverse(X),
inference(transitivity,[status(thm)],[c125,c126]) ).
cnf(c128,plain,
double_divide(identity,X) = inverse(X),
inference(transitivity,[status(thm)],[c110,c127]) ).
cnf(c129,plain,
inverse(X) = double_divide(identity,X),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(inverse(X2),X) = multiply(double_divide(identity,X2),X),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
double_divide(X2,multiply(inverse(X2),X)) = double_divide(X2,multiply(double_divide(identity,X2),X)),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
double_divide(double_divide(X2,multiply(inverse(X2),X)),inverse(identity)) = double_divide(double_divide(X2,multiply(double_divide(identity,X2),X)),inverse(identity)),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
inverse(double_divide(X,double_divide(identity,X2))) = multiply(double_divide(identity,X2),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c134,plain,
multiply(double_divide(identity,X2),X) = inverse(double_divide(X,double_divide(identity,X2))),
inference(symmetry,[status(thm)],[c133]) ).
cnf(c135,plain,
double_divide(X2,multiply(double_divide(identity,X2),X)) = double_divide(X2,inverse(double_divide(X,double_divide(identity,X2)))),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
double_divide(double_divide(X2,multiply(double_divide(identity,X2),X)),inverse(identity)) = double_divide(double_divide(X2,inverse(double_divide(X,double_divide(identity,X2)))),inverse(identity)),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
inverse(double_divide(X,double_divide(identity,X2))) = double_divide(double_divide(X,double_divide(identity,X2)),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c138,plain,
double_divide(X2,inverse(double_divide(X,double_divide(identity,X2)))) = double_divide(X2,double_divide(double_divide(X,double_divide(identity,X2)),identity)),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
double_divide(double_divide(X2,inverse(double_divide(X,double_divide(identity,X2)))),inverse(identity)) = double_divide(double_divide(X2,double_divide(double_divide(X,double_divide(identity,X2)),identity)),inverse(identity)),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c141,plain,
double_divide(double_divide(X,double_divide(identity,X2)),identity) = double_divide(double_divide(X,double_divide(identity,X2)),inverse(identity)),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
double_divide(X2,double_divide(double_divide(X,double_divide(identity,X2)),identity)) = double_divide(X2,double_divide(double_divide(X,double_divide(identity,X2)),inverse(identity))),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
double_divide(double_divide(X2,double_divide(double_divide(X,double_divide(identity,X2)),identity)),inverse(identity)) = double_divide(double_divide(X2,double_divide(double_divide(X,double_divide(identity,X2)),inverse(identity))),inverse(identity)),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
double_divide(double_divide(X2,double_divide(double_divide(X,double_divide(identity,X2)),inverse(identity))),inverse(identity)) = X,
inference(substitution,[status(thm)],[c19]) ).
cnf(c145,plain,
double_divide(double_divide(X2,double_divide(double_divide(X,double_divide(identity,X2)),identity)),inverse(identity)) = X,
inference(transitivity,[status(thm)],[c143,c144]) ).
cnf(c146,plain,
double_divide(double_divide(X2,inverse(double_divide(X,double_divide(identity,X2)))),inverse(identity)) = X,
inference(transitivity,[status(thm)],[c139,c145]) ).
cnf(c147,plain,
double_divide(double_divide(X2,multiply(double_divide(identity,X2),X)),inverse(identity)) = X,
inference(transitivity,[status(thm)],[c136,c146]) ).
cnf(c148,plain,
double_divide(double_divide(X2,multiply(inverse(X2),X)),inverse(identity)) = X,
inference(transitivity,[status(thm)],[c132,c147]) ).
cnf(c149,plain,
double_divide(double_divide(X2,multiply(inverse(X2),X)),identity) = X,
inference(transitivity,[status(thm)],[c85,c148]) ).
cnf(c150,plain,
inverse(double_divide(X2,multiply(inverse(X2),X))) = X,
inference(transitivity,[status(thm)],[c83,c149]) ).
cnf(c151,plain,
multiply(multiply(inverse(X2),X),X2) = X,
inference(transitivity,[status(thm)],[c82,c150]) ).
cnf(c152,plain,
multiply(multiply(inverse(X),X),X) = X,
inference(substitution,[status(thm)],[c151]) ).
cnf(c153,plain,
multiply(inverse(identity),X) = X,
inference(transitivity,[status(thm)],[c80,c152]) ).
cnf(c154,plain,
multiply(identity,X) = X,
inference(transitivity,[status(thm)],[c72,c153]) ).
cnf(c155,plain,
inverse(inverse(X)) = X,
inference(transitivity,[status(thm)],[c28,c154]) ).
cnf(c156,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c155]) ).
cnf(c157,plain,
double_divide(inverse(X),X) = double_divide(inverse(X),inverse(inverse(X))),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
identity = double_divide(inverse(X),inverse(inverse(X))),
inference(substitution,[status(thm)],[c31]) ).
cnf(c159,plain,
double_divide(inverse(X),inverse(inverse(X))) = identity,
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
double_divide(inverse(X),X) = identity,
inference(transitivity,[status(thm)],[c157,c159]) ).
cnf(c161,plain,
double_divide(inverse(double_divide(X,X2)),double_divide(X,X2)) = identity,
inference(substitution,[status(thm)],[c160]) ).
cnf(c162,plain,
double_divide(double_divide(inverse(double_divide(X,X2)),double_divide(X,X2)),inverse(X)) = double_divide(identity,inverse(X)),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
double_divide(X2,double_divide(double_divide(inverse(double_divide(X,X2)),double_divide(X,X2)),inverse(X))) = double_divide(X2,double_divide(identity,inverse(X))),
inference(congruence,[status(thm)],[c162]) ).
cnf(c164,plain,
double_divide(double_divide(X2,double_divide(double_divide(inverse(double_divide(X,X2)),double_divide(X,X2)),inverse(X))),inverse(identity)) = double_divide(double_divide(X2,double_divide(identity,inverse(X))),inverse(identity)),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
double_divide(identity,inverse(X)) = inverse(inverse(X)),
inference(substitution,[status(thm)],[c128]) ).
cnf(c166,plain,
double_divide(X2,double_divide(identity,inverse(X))) = double_divide(X2,inverse(inverse(X))),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
double_divide(double_divide(X2,double_divide(identity,inverse(X))),inverse(identity)) = double_divide(double_divide(X2,inverse(inverse(X))),inverse(identity)),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
double_divide(X2,inverse(inverse(X))) = double_divide(X2,X),
inference(congruence,[status(thm)],[c155]) ).
cnf(c169,plain,
double_divide(double_divide(X2,inverse(inverse(X))),inverse(identity)) = double_divide(double_divide(X2,X),inverse(identity)),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
double_divide(double_divide(X2,X),inverse(identity)) = double_divide(double_divide(X2,X),identity),
inference(congruence,[status(thm)],[c70]) ).
cnf(c171,plain,
inverse(double_divide(X2,X)) = double_divide(double_divide(X2,X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c172,plain,
double_divide(double_divide(X2,X),identity) = inverse(double_divide(X2,X)),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,plain,
double_divide(double_divide(X2,X),identity) = multiply(X,X2),
inference(transitivity,[status(thm)],[c172,c7]) ).
cnf(c174,plain,
double_divide(double_divide(X2,X),inverse(identity)) = multiply(X,X2),
inference(transitivity,[status(thm)],[c170,c173]) ).
cnf(c175,plain,
double_divide(double_divide(X2,inverse(inverse(X))),inverse(identity)) = multiply(X,X2),
inference(transitivity,[status(thm)],[c169,c174]) ).
cnf(c176,plain,
double_divide(double_divide(X2,double_divide(identity,inverse(X))),inverse(identity)) = multiply(X,X2),
inference(transitivity,[status(thm)],[c167,c175]) ).
cnf(c177,plain,
double_divide(double_divide(X2,double_divide(double_divide(inverse(double_divide(X,X2)),double_divide(X,X2)),inverse(X))),inverse(identity)) = multiply(X,X2),
inference(transitivity,[status(thm)],[c164,c176]) ).
cnf(c178,plain,
inverse(double_divide(X,X2)) = multiply(X,X2),
inference(transitivity,[status(thm)],[c21,c177]) ).
cnf(c179,plain,
multiply(X2,X) = multiply(X,X2),
inference(transitivity,[status(thm)],[c9,c178]) ).
cnf(c180,plain,
multiply(b,a) = multiply(a,b),
inference(substitution,[status(thm)],[c179]) ).
cnf(c181,plain,
multiply(a,b) = multiply(b,a),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c182,plain,
$false,
inference(resolution,[status(thm)],[c1,c181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP576-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:08:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.45 Command-line arguments: --no-flatten-goal
% 0.10/0.45
% 0.10/0.45 % SZS status Unsatisfiable
% 0.10/0.45
% 0.10/0.47 % SZS output start CNFRefutation
% See solution above
% 0.18/0.54
% 0.18/0.54 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------