%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP485-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 10:10:47 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.46s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 5
% Syntax : Number of clauses : 208 ( 208 unt; 0 nHn; 41 RR)
% Number of literals : 208 ( 207 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; 2 con; 0-2 aty)
% Number of variables : 277 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
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(inverse(X),X2)) = multiply(X2,inverse(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(X2,inverse(X)) = inverse(double_divide(inverse(X),X2)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(multiply(X2,inverse(X)),X) = multiply(inverse(double_divide(inverse(X),X2)),X),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
inverse(double_divide(inverse(X),X2)) = double_divide(double_divide(inverse(X),X2),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
multiply(inverse(double_divide(inverse(X),X2)),X) = multiply(double_divide(double_divide(inverse(X),X2),identity),X),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
inverse(identity) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
double_divide(identity,identity) = inverse(identity),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
inverse(double_divide(identity,identity)) = inverse(inverse(identity)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c17,plain,
double_divide(inverse(X),double_divide(identity,identity)) = double_divide(double_divide(X,identity),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,axiom,
identity = double_divide(A2,inverse(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(c19,plain,
identity = double_divide(identity,inverse(identity)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
double_divide(X,identity) = double_divide(X,double_divide(identity,inverse(identity))),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
double_divide(double_divide(X,identity),double_divide(identity,identity)) = double_divide(double_divide(X,double_divide(identity,inverse(identity))),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
identity = double_divide(double_divide(X2,X),inverse(double_divide(X2,X))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c23,plain,
double_divide(identity,inverse(X)) = double_divide(double_divide(double_divide(X2,X),inverse(double_divide(X2,X))),inverse(X)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
double_divide(X2,double_divide(identity,inverse(X))) = double_divide(X2,double_divide(double_divide(double_divide(X2,X),inverse(double_divide(X2,X))),inverse(X))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
double_divide(double_divide(X2,double_divide(identity,inverse(X))),double_divide(identity,identity)) = double_divide(double_divide(X2,double_divide(double_divide(double_divide(X2,X),inverse(double_divide(X2,X))),inverse(X))),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c27,plain,
double_divide(double_divide(double_divide(X2,X),X3),inverse(X)) = double_divide(double_divide(double_divide(X2,X),X3),double_divide(X,identity)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
double_divide(X3,double_divide(double_divide(double_divide(X3,X2),X),inverse(X2))) = double_divide(X3,double_divide(double_divide(double_divide(X3,X2),X),double_divide(X2,identity))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
double_divide(double_divide(X3,double_divide(double_divide(double_divide(X3,X2),X),inverse(X2))),double_divide(identity,identity)) = double_divide(double_divide(X3,double_divide(double_divide(double_divide(X3,X2),X),double_divide(X2,identity))),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,axiom,
double_divide(double_divide(A2,double_divide(double_divide(double_divide(A2,B2),C),double_divide(B2,identity))),double_divide(identity,identity)) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c31,plain,
double_divide(double_divide(X3,double_divide(double_divide(double_divide(X3,X2),X),double_divide(X2,identity))),double_divide(identity,identity)) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
double_divide(double_divide(X3,double_divide(double_divide(double_divide(X3,X2),X),inverse(X2))),double_divide(identity,identity)) = X,
inference(transitivity,[status(thm)],[c29,c31]) ).
cnf(c33,plain,
double_divide(double_divide(X2,double_divide(double_divide(double_divide(X2,X),inverse(double_divide(X2,X))),inverse(X))),double_divide(identity,identity)) = inverse(double_divide(X2,X)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
double_divide(double_divide(X2,double_divide(double_divide(double_divide(X2,X),inverse(double_divide(X2,X))),inverse(X))),double_divide(identity,identity)) = multiply(X,X2),
inference(transitivity,[status(thm)],[c33,c7]) ).
cnf(c35,plain,
double_divide(double_divide(X2,double_divide(identity,inverse(X))),double_divide(identity,identity)) = multiply(X,X2),
inference(transitivity,[status(thm)],[c25,c34]) ).
cnf(c36,plain,
double_divide(double_divide(X,double_divide(identity,inverse(identity))),double_divide(identity,identity)) = multiply(identity,X),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
inverse(double_divide(X,identity)) = multiply(identity,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c38,plain,
multiply(identity,X) = inverse(double_divide(X,identity)),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c40,plain,
double_divide(X,identity) = inverse(X),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
inverse(double_divide(X,identity)) = inverse(inverse(X)),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
multiply(identity,X) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c38,c41]) ).
cnf(c43,plain,
double_divide(double_divide(X,double_divide(identity,inverse(identity))),double_divide(identity,identity)) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c36,c42]) ).
cnf(c44,plain,
double_divide(double_divide(X,identity),double_divide(identity,identity)) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c21,c43]) ).
cnf(c45,plain,
double_divide(inverse(X),double_divide(identity,identity)) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c17,c44]) ).
cnf(c46,plain,
double_divide(inverse(identity),double_divide(identity,identity)) = inverse(inverse(identity)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
inverse(inverse(identity)) = double_divide(inverse(identity),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
inverse(identity) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c49,plain,
double_divide(inverse(identity),double_divide(identity,identity)) = double_divide(double_divide(identity,identity),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
identity = double_divide(double_divide(identity,identity),inverse(double_divide(identity,identity))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c51,plain,
double_divide(identity,identity) = double_divide(identity,double_divide(double_divide(identity,identity),inverse(double_divide(identity,identity)))),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),inverse(double_divide(identity,identity)))),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
inverse(double_divide(X,double_divide(X,identity))) = multiply(double_divide(X,identity),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c54,plain,
multiply(double_divide(X,identity),X) = inverse(double_divide(X,double_divide(X,identity))),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c56,plain,
double_divide(X,identity) = inverse(X),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
double_divide(X,double_divide(X,identity)) = double_divide(X,inverse(X)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
identity = double_divide(X,inverse(X)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c59,plain,
double_divide(X,inverse(X)) = identity,
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
double_divide(X,double_divide(X,identity)) = identity,
inference(transitivity,[status(thm)],[c57,c59]) ).
cnf(c61,plain,
inverse(double_divide(X,double_divide(X,identity))) = inverse(identity),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
inverse(identity) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c63,plain,
inverse(double_divide(X,double_divide(X,identity))) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[c61,c62]) ).
cnf(c64,plain,
multiply(double_divide(X,identity),X) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[c54,c63]) ).
cnf(c65,plain,
multiply(double_divide(identity,identity),identity) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
double_divide(identity,identity) = multiply(double_divide(identity,identity),identity),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
double_divide(double_divide(identity,identity),inverse(double_divide(identity,identity))) = double_divide(multiply(double_divide(identity,identity),identity),inverse(double_divide(identity,identity))),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
double_divide(identity,double_divide(double_divide(identity,identity),inverse(double_divide(identity,identity)))) = double_divide(identity,double_divide(multiply(double_divide(identity,identity),identity),inverse(double_divide(identity,identity)))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),inverse(double_divide(identity,identity)))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(multiply(double_divide(identity,identity),identity),inverse(double_divide(identity,identity)))),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
multiply(X,X2) = inverse(double_divide(X2,X)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c71,plain,
double_divide(multiply(X,X2),inverse(X)) = double_divide(inverse(double_divide(X2,X)),inverse(X)),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
double_divide(X2,double_divide(multiply(X,X2),inverse(X))) = double_divide(X2,double_divide(inverse(double_divide(X2,X)),inverse(X))),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
double_divide(double_divide(X2,double_divide(multiply(X,X2),inverse(X))),double_divide(identity,identity)) = double_divide(double_divide(X2,double_divide(inverse(double_divide(X2,X)),inverse(X))),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
inverse(double_divide(X2,X)) = double_divide(double_divide(X2,X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c75,plain,
double_divide(inverse(double_divide(X2,X)),inverse(X)) = double_divide(double_divide(double_divide(X2,X),identity),inverse(X)),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
double_divide(X2,double_divide(inverse(double_divide(X2,X)),inverse(X))) = double_divide(X2,double_divide(double_divide(double_divide(X2,X),identity),inverse(X))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
double_divide(double_divide(X2,double_divide(inverse(double_divide(X2,X)),inverse(X))),double_divide(identity,identity)) = double_divide(double_divide(X2,double_divide(double_divide(double_divide(X2,X),identity),inverse(X))),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
double_divide(double_divide(X2,double_divide(double_divide(double_divide(X2,X),identity),inverse(X))),double_divide(identity,identity)) = identity,
inference(substitution,[status(thm)],[c32]) ).
cnf(c79,plain,
double_divide(double_divide(X2,double_divide(inverse(double_divide(X2,X)),inverse(X))),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[c77,c78]) ).
cnf(c80,plain,
double_divide(double_divide(X2,double_divide(multiply(X,X2),inverse(X))),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[c73,c79]) ).
cnf(c81,plain,
double_divide(double_divide(identity,double_divide(multiply(double_divide(identity,identity),identity),inverse(double_divide(identity,identity)))),double_divide(identity,identity)) = identity,
inference(substitution,[status(thm)],[c80]) ).
cnf(c82,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),inverse(double_divide(identity,identity)))),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[c69,c81]) ).
cnf(c83,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[c52,c82]) ).
cnf(c84,plain,
double_divide(inverse(identity),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[c49,c83]) ).
cnf(c85,plain,
inverse(inverse(identity)) = identity,
inference(transitivity,[status(thm)],[c47,c84]) ).
cnf(c86,plain,
inverse(double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[c15,c85]) ).
cnf(c87,plain,
identity = inverse(double_divide(identity,identity)),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
double_divide(double_divide(inverse(X),X2),identity) = double_divide(double_divide(inverse(X),X2),inverse(double_divide(identity,identity))),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
multiply(double_divide(double_divide(inverse(X),X2),identity),X) = multiply(double_divide(double_divide(inverse(X),X2),inverse(double_divide(identity,identity))),X),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
inverse(double_divide(X,double_divide(double_divide(inverse(X),X2),inverse(double_divide(identity,identity))))) = multiply(double_divide(double_divide(inverse(X),X2),inverse(double_divide(identity,identity))),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c91,plain,
multiply(double_divide(double_divide(inverse(X),X2),inverse(double_divide(identity,identity))),X) = inverse(double_divide(X,double_divide(double_divide(inverse(X),X2),inverse(double_divide(identity,identity))))),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
inverse(identity) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c93,plain,
double_divide(identity,identity) = inverse(identity),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
identity = inverse(double_divide(identity,identity)),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c95,plain,
inverse(identity) = inverse(inverse(double_divide(identity,identity))),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
double_divide(inverse(double_divide(identity,identity)),double_divide(identity,identity)) = inverse(inverse(double_divide(identity,identity))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c97,plain,
inverse(inverse(double_divide(identity,identity))) = double_divide(inverse(double_divide(identity,identity)),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
double_divide(inverse(double_divide(identity,identity)),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,identity)),
inference(congruence,[status(thm)],[c86]) ).
cnf(c99,plain,
double_divide(identity,double_divide(identity,identity)) = identity,
inference(substitution,[status(thm)],[c60]) ).
cnf(c100,plain,
double_divide(inverse(double_divide(identity,identity)),double_divide(identity,identity)) = identity,
inference(transitivity,[status(thm)],[c98,c99]) ).
cnf(c101,plain,
inverse(inverse(double_divide(identity,identity))) = identity,
inference(transitivity,[status(thm)],[c97,c100]) ).
cnf(c102,plain,
inverse(identity) = identity,
inference(transitivity,[status(thm)],[c95,c101]) ).
cnf(c103,plain,
double_divide(identity,identity) = identity,
inference(transitivity,[status(thm)],[c93,c102]) ).
cnf(c104,plain,
double_divide(X,double_divide(identity,identity)) = double_divide(X,identity),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c106,plain,
double_divide(X,identity) = inverse(X),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
double_divide(X,double_divide(identity,identity)) = inverse(X),
inference(transitivity,[status(thm)],[c104,c106]) ).
cnf(c108,plain,
double_divide(double_divide(X,double_divide(double_divide(inverse(X),X2),inverse(double_divide(identity,identity)))),double_divide(identity,identity)) = inverse(double_divide(X,double_divide(double_divide(inverse(X),X2),inverse(double_divide(identity,identity))))),
inference(substitution,[status(thm)],[c107]) ).
cnf(c109,plain,
inverse(double_divide(X,double_divide(double_divide(inverse(X),X2),inverse(double_divide(identity,identity))))) = double_divide(double_divide(X,double_divide(double_divide(inverse(X),X2),inverse(double_divide(identity,identity)))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
inverse(X) = double_divide(X,double_divide(identity,identity)),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c111,plain,
double_divide(inverse(X),X2) = double_divide(double_divide(X,double_divide(identity,identity)),X2),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
double_divide(double_divide(inverse(X),X2),inverse(double_divide(identity,identity))) = double_divide(double_divide(double_divide(X,double_divide(identity,identity)),X2),inverse(double_divide(identity,identity))),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
double_divide(X,double_divide(double_divide(inverse(X),X2),inverse(double_divide(identity,identity)))) = double_divide(X,double_divide(double_divide(double_divide(X,double_divide(identity,identity)),X2),inverse(double_divide(identity,identity)))),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
double_divide(double_divide(X,double_divide(double_divide(inverse(X),X2),inverse(double_divide(identity,identity)))),double_divide(identity,identity)) = double_divide(double_divide(X,double_divide(double_divide(double_divide(X,double_divide(identity,identity)),X2),inverse(double_divide(identity,identity)))),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
double_divide(double_divide(X,double_divide(double_divide(double_divide(X,double_divide(identity,identity)),X2),inverse(double_divide(identity,identity)))),double_divide(identity,identity)) = X2,
inference(substitution,[status(thm)],[c32]) ).
cnf(c116,plain,
double_divide(double_divide(X,double_divide(double_divide(inverse(X),X2),inverse(double_divide(identity,identity)))),double_divide(identity,identity)) = X2,
inference(transitivity,[status(thm)],[c114,c115]) ).
cnf(c117,plain,
inverse(double_divide(X,double_divide(double_divide(inverse(X),X2),inverse(double_divide(identity,identity))))) = X2,
inference(transitivity,[status(thm)],[c109,c116]) ).
cnf(c118,plain,
multiply(double_divide(double_divide(inverse(X),X2),inverse(double_divide(identity,identity))),X) = X2,
inference(transitivity,[status(thm)],[c91,c117]) ).
cnf(c119,plain,
multiply(double_divide(double_divide(inverse(X),X2),identity),X) = X2,
inference(transitivity,[status(thm)],[c89,c118]) ).
cnf(c120,plain,
multiply(inverse(double_divide(inverse(X),X2)),X) = X2,
inference(transitivity,[status(thm)],[c12,c119]) ).
cnf(c121,plain,
multiply(multiply(X2,inverse(X)),X) = X2,
inference(transitivity,[status(thm)],[c10,c120]) ).
cnf(c122,plain,
multiply(multiply(multiply(identity,X2),inverse(X)),X) = multiply(identity,X2),
inference(substitution,[status(thm)],[c121]) ).
cnf(c123,plain,
multiply(identity,X2) = multiply(multiply(multiply(identity,X2),inverse(X)),X),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
double_divide(double_divide(X,double_divide(identity,inverse(multiply(identity,X2)))),double_divide(identity,identity)) = multiply(multiply(identity,X2),X),
inference(substitution,[status(thm)],[c35]) ).
cnf(c125,plain,
multiply(multiply(identity,X2),X) = double_divide(double_divide(X,double_divide(identity,inverse(multiply(identity,X2)))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
multiply(multiply(inverse(multiply(identity,X2)),inverse(X)),X) = inverse(multiply(identity,X2)),
inference(substitution,[status(thm)],[c121]) ).
cnf(c127,plain,
inverse(multiply(identity,X2)) = multiply(multiply(inverse(multiply(identity,X2)),inverse(X)),X),
inference(symmetry,[status(thm)],[c126]) ).
cnf(c128,plain,
double_divide(double_divide(X,double_divide(identity,inverse(inverse(multiply(identity,X2))))),double_divide(identity,identity)) = multiply(inverse(multiply(identity,X2)),X),
inference(substitution,[status(thm)],[c35]) ).
cnf(c129,plain,
multiply(inverse(multiply(identity,X2)),X) = double_divide(double_divide(X,double_divide(identity,inverse(inverse(multiply(identity,X2))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(multiply(inverse(inverse(multiply(identity,X))),inverse(X)),X) = inverse(inverse(multiply(identity,X))),
inference(substitution,[status(thm)],[c121]) ).
cnf(c131,plain,
inverse(inverse(multiply(identity,X))) = multiply(multiply(inverse(inverse(multiply(identity,X))),inverse(X)),X),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
inverse(multiply(identity,X)) = inverse(inverse(inverse(X))),
inference(congruence,[status(thm)],[c42]) ).
cnf(c133,plain,
inverse(inverse(multiply(identity,X))) = inverse(inverse(inverse(inverse(X)))),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
multiply(inverse(inverse(multiply(identity,X))),inverse(X)) = multiply(inverse(inverse(inverse(inverse(X)))),inverse(X)),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
double_divide(double_divide(X,double_divide(identity,inverse(double_divide(multiply(X2,X),inverse(X2))))),double_divide(identity,identity)) = multiply(double_divide(multiply(X2,X),inverse(X2)),X),
inference(substitution,[status(thm)],[c35]) ).
cnf(c136,plain,
multiply(double_divide(multiply(X2,X),inverse(X2)),X) = double_divide(double_divide(X,double_divide(identity,inverse(double_divide(multiply(X2,X),inverse(X2))))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
double_divide(double_divide(X,double_divide(multiply(X2,X),inverse(X2))),double_divide(identity,identity)) = identity,
inference(substitution,[status(thm)],[c80]) ).
cnf(c138,plain,
identity = double_divide(double_divide(X,double_divide(multiply(X2,X),inverse(X2))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
double_divide(identity,inverse(double_divide(multiply(X2,X),inverse(X2)))) = double_divide(double_divide(double_divide(X,double_divide(multiply(X2,X),inverse(X2))),double_divide(identity,identity)),inverse(double_divide(multiply(X2,X),inverse(X2)))),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
double_divide(X,double_divide(identity,inverse(double_divide(multiply(X2,X),inverse(X2))))) = double_divide(X,double_divide(double_divide(double_divide(X,double_divide(multiply(X2,X),inverse(X2))),double_divide(identity,identity)),inverse(double_divide(multiply(X2,X),inverse(X2))))),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
double_divide(double_divide(X,double_divide(identity,inverse(double_divide(multiply(X2,X),inverse(X2))))),double_divide(identity,identity)) = double_divide(double_divide(X,double_divide(double_divide(double_divide(X,double_divide(multiply(X2,X),inverse(X2))),double_divide(identity,identity)),inverse(double_divide(multiply(X2,X),inverse(X2))))),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
double_divide(double_divide(X,double_divide(double_divide(double_divide(X,double_divide(multiply(X2,X),inverse(X2))),double_divide(identity,identity)),inverse(double_divide(multiply(X2,X),inverse(X2))))),double_divide(identity,identity)) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c32]) ).
cnf(c143,plain,
double_divide(double_divide(X,double_divide(identity,inverse(double_divide(multiply(X2,X),inverse(X2))))),double_divide(identity,identity)) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[c141,c142]) ).
cnf(c144,plain,
multiply(double_divide(multiply(X2,X),inverse(X2)),X) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[c136,c143]) ).
cnf(c145,plain,
multiply(double_divide(multiply(identity,X),inverse(identity)),X) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c144]) ).
cnf(c146,plain,
double_divide(identity,identity) = multiply(double_divide(multiply(identity,X),inverse(identity)),X),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
inverse(identity) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c148,plain,
double_divide(multiply(identity,X),inverse(identity)) = double_divide(multiply(identity,X),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
multiply(double_divide(multiply(identity,X),inverse(identity)),X) = multiply(double_divide(multiply(identity,X),double_divide(identity,identity)),X),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
double_divide(multiply(identity,X),double_divide(identity,identity)) = inverse(multiply(identity,X)),
inference(substitution,[status(thm)],[c107]) ).
cnf(c151,plain,
multiply(double_divide(multiply(identity,X),double_divide(identity,identity)),X) = multiply(inverse(multiply(identity,X)),X),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
inverse(multiply(identity,X)) = inverse(inverse(inverse(X))),
inference(congruence,[status(thm)],[c42]) ).
cnf(c153,plain,
multiply(inverse(multiply(identity,X)),X) = multiply(inverse(inverse(inverse(X))),X),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
multiply(double_divide(multiply(identity,X),double_divide(identity,identity)),X) = multiply(inverse(inverse(inverse(X))),X),
inference(transitivity,[status(thm)],[c151,c153]) ).
cnf(c155,plain,
multiply(double_divide(multiply(identity,X),inverse(identity)),X) = multiply(inverse(inverse(inverse(X))),X),
inference(transitivity,[status(thm)],[c149,c154]) ).
cnf(c156,plain,
double_divide(identity,identity) = multiply(inverse(inverse(inverse(X))),X),
inference(transitivity,[status(thm)],[c146,c155]) ).
cnf(c157,plain,
double_divide(identity,identity) = multiply(inverse(inverse(inverse(inverse(X)))),inverse(X)),
inference(substitution,[status(thm)],[c156]) ).
cnf(c158,plain,
multiply(inverse(inverse(inverse(inverse(X)))),inverse(X)) = double_divide(identity,identity),
inference(symmetry,[status(thm)],[c157]) ).
cnf(c159,plain,
multiply(inverse(inverse(multiply(identity,X))),inverse(X)) = double_divide(identity,identity),
inference(transitivity,[status(thm)],[c134,c158]) ).
cnf(c160,plain,
multiply(multiply(inverse(inverse(multiply(identity,X))),inverse(X)),X) = multiply(double_divide(identity,identity),X),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
multiply(double_divide(identity,identity),X) = multiply(identity,X),
inference(congruence,[status(thm)],[c103]) ).
cnf(c162,plain,
multiply(multiply(inverse(inverse(multiply(identity,X))),inverse(X)),X) = multiply(identity,X),
inference(transitivity,[status(thm)],[c160,c161]) ).
cnf(c163,plain,
inverse(inverse(multiply(identity,X))) = multiply(identity,X),
inference(transitivity,[status(thm)],[c131,c162]) ).
cnf(c164,plain,
double_divide(identity,inverse(inverse(multiply(identity,X)))) = double_divide(identity,multiply(identity,X)),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
double_divide(X,double_divide(identity,inverse(inverse(multiply(identity,X2))))) = double_divide(X,double_divide(identity,multiply(identity,X2))),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
double_divide(double_divide(X,double_divide(identity,inverse(inverse(multiply(identity,X2))))),double_divide(identity,identity)) = double_divide(double_divide(X,double_divide(identity,multiply(identity,X2))),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
double_divide(double_divide(X,double_divide(identity,multiply(identity,X2))),double_divide(identity,identity)) = inverse(double_divide(X,double_divide(identity,multiply(identity,X2)))),
inference(substitution,[status(thm)],[c107]) ).
cnf(c168,plain,
inverse(double_divide(X,double_divide(identity,multiply(identity,X2)))) = multiply(double_divide(identity,multiply(identity,X2)),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c169,plain,
identity = double_divide(identity,identity),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c170,plain,
double_divide(identity,multiply(identity,X)) = double_divide(double_divide(identity,identity),multiply(identity,X)),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
multiply(double_divide(identity,multiply(identity,X2)),X) = multiply(double_divide(double_divide(identity,identity),multiply(identity,X2)),X),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
double_divide(double_divide(identity,identity),multiply(identity,X)) = double_divide(identity,multiply(identity,X)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c173,plain,
multiply(double_divide(double_divide(identity,identity),multiply(identity,X2)),X) = multiply(double_divide(identity,multiply(identity,X2)),X),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
inverse(double_divide(X,double_divide(identity,multiply(identity,X2)))) = multiply(double_divide(identity,multiply(identity,X2)),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c175,plain,
multiply(double_divide(identity,multiply(identity,X2)),X) = inverse(double_divide(X,double_divide(identity,multiply(identity,X2)))),
inference(symmetry,[status(thm)],[c174]) ).
cnf(c176,plain,
double_divide(double_divide(X,double_divide(identity,multiply(identity,X2))),double_divide(identity,identity)) = inverse(double_divide(X,double_divide(identity,multiply(identity,X2)))),
inference(substitution,[status(thm)],[c107]) ).
cnf(c177,plain,
inverse(double_divide(X,double_divide(identity,multiply(identity,X2)))) = double_divide(double_divide(X,double_divide(identity,multiply(identity,X2))),double_divide(identity,identity)),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
double_divide(identity,multiply(identity,X)) = double_divide(identity,inverse(inverse(X))),
inference(congruence,[status(thm)],[c42]) ).
cnf(c179,plain,
double_divide(X2,double_divide(identity,multiply(identity,X))) = double_divide(X2,double_divide(identity,inverse(inverse(X)))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
double_divide(double_divide(X2,double_divide(identity,multiply(identity,X))),double_divide(identity,identity)) = double_divide(double_divide(X2,double_divide(identity,inverse(inverse(X)))),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
double_divide(double_divide(X2,double_divide(identity,inverse(inverse(X)))),double_divide(identity,identity)) = multiply(inverse(X),X2),
inference(substitution,[status(thm)],[c35]) ).
cnf(c182,plain,
double_divide(double_divide(X2,double_divide(identity,multiply(identity,X))),double_divide(identity,identity)) = multiply(inverse(X),X2),
inference(transitivity,[status(thm)],[c180,c181]) ).
cnf(c183,plain,
double_divide(double_divide(X,double_divide(identity,multiply(identity,X2))),double_divide(identity,identity)) = multiply(inverse(X2),X),
inference(substitution,[status(thm)],[c182]) ).
cnf(c184,plain,
inverse(double_divide(X,double_divide(identity,multiply(identity,X2)))) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c177,c183]) ).
cnf(c185,plain,
multiply(double_divide(identity,multiply(identity,X2)),X) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c175,c184]) ).
cnf(c186,plain,
multiply(double_divide(double_divide(identity,identity),multiply(identity,X2)),X) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c173,c185]) ).
cnf(c187,plain,
multiply(double_divide(identity,multiply(identity,X2)),X) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c171,c186]) ).
cnf(c188,plain,
inverse(double_divide(X,double_divide(identity,multiply(identity,X2)))) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c168,c187]) ).
cnf(c189,plain,
double_divide(double_divide(X,double_divide(identity,multiply(identity,X2))),double_divide(identity,identity)) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c167,c188]) ).
cnf(c190,plain,
double_divide(double_divide(X,double_divide(identity,inverse(inverse(multiply(identity,X2))))),double_divide(identity,identity)) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c166,c189]) ).
cnf(c191,plain,
multiply(inverse(multiply(identity,X2)),X) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c129,c190]) ).
cnf(c192,plain,
multiply(inverse(multiply(identity,X2)),inverse(X)) = multiply(inverse(X2),inverse(X)),
inference(substitution,[status(thm)],[c191]) ).
cnf(c193,plain,
multiply(multiply(inverse(multiply(identity,X2)),inverse(X)),X) = multiply(multiply(inverse(X2),inverse(X)),X),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
multiply(multiply(inverse(X2),inverse(X)),X) = inverse(X2),
inference(substitution,[status(thm)],[c121]) ).
cnf(c195,plain,
multiply(multiply(inverse(multiply(identity,X2)),inverse(X)),X) = inverse(X2),
inference(transitivity,[status(thm)],[c193,c194]) ).
cnf(c196,plain,
inverse(multiply(identity,X)) = inverse(X),
inference(transitivity,[status(thm)],[c127,c195]) ).
cnf(c197,plain,
double_divide(identity,inverse(multiply(identity,X))) = double_divide(identity,inverse(X)),
inference(congruence,[status(thm)],[c196]) ).
cnf(c198,plain,
double_divide(X,double_divide(identity,inverse(multiply(identity,X2)))) = double_divide(X,double_divide(identity,inverse(X2))),
inference(congruence,[status(thm)],[c197]) ).
cnf(c199,plain,
double_divide(double_divide(X,double_divide(identity,inverse(multiply(identity,X2)))),double_divide(identity,identity)) = double_divide(double_divide(X,double_divide(identity,inverse(X2))),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
double_divide(double_divide(X,double_divide(identity,inverse(X2))),double_divide(identity,identity)) = multiply(X2,X),
inference(substitution,[status(thm)],[c35]) ).
cnf(c201,plain,
double_divide(double_divide(X,double_divide(identity,inverse(multiply(identity,X2)))),double_divide(identity,identity)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c199,c200]) ).
cnf(c202,plain,
multiply(multiply(identity,X2),X) = multiply(X2,X),
inference(transitivity,[status(thm)],[c125,c201]) ).
cnf(c203,plain,
multiply(multiply(identity,X2),inverse(X)) = multiply(X2,inverse(X)),
inference(substitution,[status(thm)],[c202]) ).
cnf(c204,plain,
multiply(multiply(multiply(identity,X2),inverse(X)),X) = multiply(multiply(X2,inverse(X)),X),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
multiply(multiply(multiply(identity,X2),inverse(X)),X) = X2,
inference(transitivity,[status(thm)],[c204,c121]) ).
cnf(c206,plain,
multiply(identity,X) = X,
inference(transitivity,[status(thm)],[c123,c205]) ).
cnf(c207,plain,
multiply(identity,a2) = a2,
inference(substitution,[status(thm)],[c206]) ).
cnf(c208,plain,
$false,
inference(resolution,[status(thm)],[c1,c207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP485-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 10:10:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.46 Command-line arguments: --flatten --complete-subsets
% 0.13/0.46
% 0.13/0.46 % SZS status Unsatisfiable
% 0.13/0.46
% 0.13/0.47 % SZS output start CNFRefutation
% See solution above
% 0.64/0.56
% 0.64/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------