%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP492-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:10:49 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.45s
% Output : CNFRefutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 99
% Number of leaves : 5
% Syntax : Number of clauses : 292 ( 292 unt; 0 nHn; 21 RR)
% Number of literals : 292 ( 291 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 503 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(c2,axiom,
inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(c3,plain,
inverse(multiply(inverse(X),X2)) = double_divide(multiply(inverse(X),X2),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
double_divide(identity,inverse(multiply(inverse(X),X2))) = double_divide(identity,double_divide(multiply(inverse(X),X2),identity)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
double_divide(double_divide(identity,X2),double_divide(identity,inverse(multiply(inverse(X),X2)))) = double_divide(double_divide(identity,X2),double_divide(identity,double_divide(multiply(inverse(X),X2),identity))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
identity = double_divide(A2,inverse(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(c7,plain,
identity = double_divide(X,inverse(X)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
double_divide(multiply(inverse(X),X2),identity) = double_divide(multiply(inverse(X),X2),double_divide(X,inverse(X))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
double_divide(identity,double_divide(multiply(inverse(X),X2),identity)) = double_divide(identity,double_divide(multiply(inverse(X),X2),double_divide(X,inverse(X)))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
double_divide(double_divide(identity,X2),double_divide(identity,double_divide(multiply(inverse(X),X2),identity))) = double_divide(double_divide(identity,X2),double_divide(identity,double_divide(multiply(inverse(X),X2),double_divide(X,inverse(X))))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
inverse(double_divide(X2,X)) = double_divide(double_divide(X2,X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,axiom,
multiply(A2,B) = double_divide(double_divide(B,A2),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c13,plain,
multiply(X,X2) = double_divide(double_divide(X2,X),identity),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
double_divide(double_divide(X2,X),identity) = multiply(X,X2),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
inverse(double_divide(X2,X)) = multiply(X,X2),
inference(transitivity,[status(thm)],[c11,c14]) ).
cnf(c16,plain,
multiply(X,X2) = inverse(double_divide(X2,X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
double_divide(multiply(X,X2),double_divide(X3,X)) = double_divide(inverse(double_divide(X2,X)),double_divide(X3,X)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
double_divide(identity,double_divide(multiply(X2,X3),double_divide(X,X2))) = double_divide(identity,double_divide(inverse(double_divide(X3,X2)),double_divide(X,X2))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
double_divide(double_divide(identity,X3),double_divide(identity,double_divide(multiply(X2,X3),double_divide(X,X2)))) = double_divide(double_divide(identity,X3),double_divide(identity,double_divide(inverse(double_divide(X3,X2)),double_divide(X,X2)))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
inverse(double_divide(X2,X)) = double_divide(double_divide(X2,X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,plain,
double_divide(inverse(double_divide(X3,X2)),double_divide(X,X2)) = double_divide(double_divide(double_divide(X3,X2),identity),double_divide(X,X2)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
double_divide(identity,double_divide(inverse(double_divide(X3,X2)),double_divide(X,X2))) = double_divide(identity,double_divide(double_divide(double_divide(X3,X2),identity),double_divide(X,X2))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
double_divide(double_divide(identity,X3),double_divide(identity,double_divide(inverse(double_divide(X3,X2)),double_divide(X,X2)))) = double_divide(double_divide(identity,X3),double_divide(identity,double_divide(double_divide(double_divide(X3,X2),identity),double_divide(X,X2)))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,axiom,
double_divide(double_divide(identity,A2),double_divide(identity,double_divide(double_divide(double_divide(A2,B2),identity),double_divide(C,B2)))) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c25,plain,
double_divide(double_divide(identity,X3),double_divide(identity,double_divide(double_divide(double_divide(X3,X2),identity),double_divide(X,X2)))) = X,
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
double_divide(double_divide(identity,X3),double_divide(identity,double_divide(inverse(double_divide(X3,X2)),double_divide(X,X2)))) = X,
inference(transitivity,[status(thm)],[c23,c25]) ).
cnf(c27,plain,
double_divide(double_divide(identity,X3),double_divide(identity,double_divide(multiply(X2,X3),double_divide(X,X2)))) = X,
inference(transitivity,[status(thm)],[c19,c26]) ).
cnf(c28,plain,
double_divide(double_divide(identity,X2),double_divide(identity,double_divide(multiply(inverse(X),X2),double_divide(X,inverse(X))))) = X,
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
double_divide(double_divide(identity,X2),double_divide(identity,double_divide(multiply(inverse(X),X2),identity))) = X,
inference(transitivity,[status(thm)],[c10,c28]) ).
cnf(c30,plain,
double_divide(double_divide(identity,X2),double_divide(identity,inverse(multiply(inverse(X),X2)))) = X,
inference(transitivity,[status(thm)],[c5,c29]) ).
cnf(c31,plain,
double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(inverse(inverse(X2))),X)))) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
inverse(inverse(X2)) = double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(inverse(inverse(X2))),X)))),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
inverse(multiply(inverse(inverse(inverse(X2))),X)) = double_divide(multiply(inverse(inverse(inverse(X2))),X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c34,plain,
double_divide(identity,inverse(multiply(inverse(inverse(inverse(X2))),X))) = double_divide(identity,double_divide(multiply(inverse(inverse(inverse(X2))),X),identity)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(inverse(inverse(X2))),X)))) = double_divide(double_divide(identity,X),double_divide(identity,double_divide(multiply(inverse(inverse(inverse(X2))),X),identity))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
inverse(double_divide(X,identity)) = multiply(identity,X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c37,plain,
multiply(identity,X) = inverse(double_divide(X,identity)),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c39,plain,
double_divide(X,identity) = inverse(X),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
inverse(double_divide(X,identity)) = inverse(inverse(X)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(identity,X) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c37,c40]) ).
cnf(c42,plain,
multiply(identity,inverse(X)) = inverse(inverse(inverse(X))),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
inverse(inverse(inverse(X))) = multiply(identity,inverse(X)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
double_divide(X,inverse(inverse(inverse(X)))) = double_divide(X,multiply(identity,inverse(X))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(inverse(identity)),X)))) = inverse(identity),
inference(substitution,[status(thm)],[c30]) ).
cnf(c46,plain,
inverse(identity) = double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(inverse(identity)),X)))),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
inverse(multiply(inverse(inverse(identity)),X)) = double_divide(multiply(inverse(inverse(identity)),X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c48,plain,
double_divide(identity,inverse(multiply(inverse(inverse(identity)),X))) = double_divide(identity,double_divide(multiply(inverse(inverse(identity)),X),identity)),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(inverse(identity)),X)))) = double_divide(double_divide(identity,X),double_divide(identity,double_divide(multiply(inverse(inverse(identity)),X),identity))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
inverse(double_divide(X,inverse(X))) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c51,plain,
multiply(inverse(X),X) = inverse(double_divide(X,inverse(X))),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
identity = double_divide(X,inverse(X)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c53,plain,
double_divide(X,inverse(X)) = identity,
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
inverse(double_divide(X,inverse(X))) = inverse(identity),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(inverse(X),X) = inverse(identity),
inference(transitivity,[status(thm)],[c51,c54]) ).
cnf(c56,plain,
inverse(identity) = multiply(inverse(X),X),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
inverse(inverse(identity)) = inverse(multiply(inverse(X),X)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
double_divide(identity,inverse(inverse(identity))) = double_divide(identity,inverse(multiply(inverse(X),X))),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
double_divide(double_divide(identity,X),double_divide(identity,inverse(inverse(identity)))) = double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(X),X)))) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c61,plain,
double_divide(double_divide(identity,X),double_divide(identity,inverse(inverse(identity)))) = X,
inference(transitivity,[status(thm)],[c59,c60]) ).
cnf(c62,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))) = double_divide(identity,inverse(inverse(identity))),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
double_divide(identity,inverse(inverse(identity))) = double_divide(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
identity = double_divide(identity,inverse(identity)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c65,plain,
double_divide(identity,double_divide(identity,inverse(inverse(identity)))) = double_divide(double_divide(identity,inverse(identity)),double_divide(identity,inverse(inverse(identity)))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
double_divide(double_divide(identity,inverse(identity)),double_divide(identity,inverse(inverse(identity)))) = inverse(identity),
inference(substitution,[status(thm)],[c61]) ).
cnf(c67,plain,
double_divide(identity,double_divide(identity,inverse(inverse(identity)))) = inverse(identity),
inference(transitivity,[status(thm)],[c65,c66]) ).
cnf(c68,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))) = double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
inverse(identity) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c70,plain,
double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = double_divide(double_divide(identity,identity),double_divide(identity,inverse(inverse(identity)))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
double_divide(double_divide(identity,identity),double_divide(identity,inverse(inverse(identity)))) = identity,
inference(substitution,[status(thm)],[c61]) ).
cnf(c72,plain,
double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = identity,
inference(transitivity,[status(thm)],[c70,c71]) ).
cnf(c73,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))) = identity,
inference(transitivity,[status(thm)],[c68,c72]) ).
cnf(c74,plain,
double_divide(identity,inverse(inverse(identity))) = identity,
inference(transitivity,[status(thm)],[c63,c73]) ).
cnf(c75,plain,
identity = double_divide(identity,inverse(inverse(identity))),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
double_divide(multiply(inverse(inverse(identity)),X),identity) = double_divide(multiply(inverse(inverse(identity)),X),double_divide(identity,inverse(inverse(identity)))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
double_divide(identity,double_divide(multiply(inverse(inverse(identity)),X),identity)) = double_divide(identity,double_divide(multiply(inverse(inverse(identity)),X),double_divide(identity,inverse(inverse(identity))))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(multiply(inverse(inverse(identity)),X),identity))) = double_divide(double_divide(identity,X),double_divide(identity,double_divide(multiply(inverse(inverse(identity)),X),double_divide(identity,inverse(inverse(identity)))))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(multiply(inverse(inverse(identity)),X),double_divide(identity,inverse(inverse(identity)))))) = identity,
inference(substitution,[status(thm)],[c27]) ).
cnf(c80,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(multiply(inverse(inverse(identity)),X),identity))) = identity,
inference(transitivity,[status(thm)],[c78,c79]) ).
cnf(c81,plain,
double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(inverse(identity)),X)))) = identity,
inference(transitivity,[status(thm)],[c49,c80]) ).
cnf(c82,plain,
inverse(identity) = identity,
inference(transitivity,[status(thm)],[c46,c81]) ).
cnf(c83,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(identity,inverse(X)) = multiply(inverse(identity),inverse(X)),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
double_divide(X,multiply(identity,inverse(X))) = double_divide(X,multiply(inverse(identity),inverse(X))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
inverse(double_divide(identity,X)) = multiply(X,identity),
inference(substitution,[status(thm)],[c15]) ).
cnf(c87,plain,
multiply(X,identity) = inverse(double_divide(identity,X)),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
inverse(double_divide(identity,X)) = double_divide(double_divide(identity,X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c89,plain,
identity = double_divide(identity,inverse(inverse(identity))),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c90,plain,
double_divide(double_divide(identity,X),identity) = double_divide(double_divide(identity,X),double_divide(identity,inverse(inverse(identity)))),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
double_divide(double_divide(identity,X),identity) = X,
inference(transitivity,[status(thm)],[c90,c61]) ).
cnf(c92,plain,
inverse(double_divide(identity,X)) = X,
inference(transitivity,[status(thm)],[c88,c91]) ).
cnf(c93,plain,
multiply(X,identity) = X,
inference(transitivity,[status(thm)],[c87,c92]) ).
cnf(c94,plain,
multiply(double_divide(identity,inverse(X)),identity) = double_divide(identity,inverse(X)),
inference(substitution,[status(thm)],[c93]) ).
cnf(c95,plain,
double_divide(identity,inverse(X)) = multiply(double_divide(identity,inverse(X)),identity),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
inverse(double_divide(identity,double_divide(identity,inverse(X)))) = multiply(double_divide(identity,inverse(X)),identity),
inference(substitution,[status(thm)],[c15]) ).
cnf(c97,plain,
multiply(double_divide(identity,inverse(X)),identity) = inverse(double_divide(identity,double_divide(identity,inverse(X)))),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
inverse(double_divide(identity,double_divide(identity,inverse(X)))) = double_divide(double_divide(identity,double_divide(identity,inverse(X))),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c99,plain,
identity = double_divide(identity,inverse(identity)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c100,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X))),identity) = double_divide(double_divide(identity,double_divide(identity,inverse(X))),double_divide(identity,inverse(identity))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
X = multiply(X,identity),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c102,plain,
multiply(X,double_divide(identity,X)) = multiply(multiply(X,identity),double_divide(identity,X)),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c104,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
multiply(multiply(X2,X),double_divide(X,X2)) = multiply(inverse(double_divide(X,X2)),double_divide(X,X2)),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
multiply(inverse(double_divide(X,X2)),double_divide(X,X2)) = inverse(identity),
inference(substitution,[status(thm)],[c55]) ).
cnf(c107,plain,
multiply(multiply(X2,X),double_divide(X,X2)) = inverse(identity),
inference(transitivity,[status(thm)],[c105,c106]) ).
cnf(c108,plain,
multiply(multiply(X,identity),double_divide(identity,X)) = inverse(identity),
inference(substitution,[status(thm)],[c107]) ).
cnf(c109,plain,
multiply(multiply(X,identity),double_divide(identity,X)) = identity,
inference(transitivity,[status(thm)],[c108,c82]) ).
cnf(c110,plain,
multiply(X,double_divide(identity,X)) = identity,
inference(transitivity,[status(thm)],[c102,c109]) ).
cnf(c111,plain,
multiply(inverse(X),double_divide(identity,inverse(X))) = identity,
inference(substitution,[status(thm)],[c110]) ).
cnf(c112,plain,
identity = multiply(inverse(X),double_divide(identity,inverse(X))),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
inverse(identity) = inverse(multiply(inverse(X),double_divide(identity,inverse(X)))),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
double_divide(identity,inverse(identity)) = double_divide(identity,inverse(multiply(inverse(X),double_divide(identity,inverse(X))))),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X))),double_divide(identity,inverse(identity))) = double_divide(double_divide(identity,double_divide(identity,inverse(X))),double_divide(identity,inverse(multiply(inverse(X),double_divide(identity,inverse(X)))))),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X))),double_divide(identity,inverse(multiply(inverse(X),double_divide(identity,inverse(X)))))) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c117,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X))),double_divide(identity,inverse(identity))) = X,
inference(transitivity,[status(thm)],[c115,c116]) ).
cnf(c118,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(X))),identity) = X,
inference(transitivity,[status(thm)],[c100,c117]) ).
cnf(c119,plain,
inverse(double_divide(identity,double_divide(identity,inverse(X)))) = X,
inference(transitivity,[status(thm)],[c98,c118]) ).
cnf(c120,plain,
multiply(double_divide(identity,inverse(X)),identity) = X,
inference(transitivity,[status(thm)],[c97,c119]) ).
cnf(c121,plain,
double_divide(identity,inverse(X)) = X,
inference(transitivity,[status(thm)],[c95,c120]) ).
cnf(c122,plain,
double_divide(identity,inverse(multiply(inverse(X),inverse(X2)))) = multiply(inverse(X),inverse(X2)),
inference(substitution,[status(thm)],[c121]) ).
cnf(c123,plain,
multiply(inverse(X),inverse(X2)) = double_divide(identity,inverse(multiply(inverse(X),inverse(X2)))),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
double_divide(X2,multiply(inverse(X),inverse(X2))) = double_divide(X2,double_divide(identity,inverse(multiply(inverse(X),inverse(X2))))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
X = double_divide(identity,inverse(X)),
inference(symmetry,[status(thm)],[c121]) ).
cnf(c126,plain,
double_divide(X2,double_divide(identity,inverse(multiply(inverse(X),inverse(X2))))) = double_divide(double_divide(identity,inverse(X2)),double_divide(identity,inverse(multiply(inverse(X),inverse(X2))))),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
double_divide(double_divide(identity,inverse(X2)),double_divide(identity,inverse(multiply(inverse(X),inverse(X2))))) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c128,plain,
double_divide(X2,double_divide(identity,inverse(multiply(inverse(X),inverse(X2))))) = X,
inference(transitivity,[status(thm)],[c126,c127]) ).
cnf(c129,plain,
double_divide(X2,multiply(inverse(X),inverse(X2))) = X,
inference(transitivity,[status(thm)],[c124,c128]) ).
cnf(c130,plain,
double_divide(X,multiply(inverse(identity),inverse(X))) = identity,
inference(substitution,[status(thm)],[c129]) ).
cnf(c131,plain,
double_divide(X,multiply(identity,inverse(X))) = identity,
inference(transitivity,[status(thm)],[c85,c130]) ).
cnf(c132,plain,
double_divide(X,inverse(inverse(inverse(X)))) = identity,
inference(transitivity,[status(thm)],[c44,c131]) ).
cnf(c133,plain,
identity = double_divide(X,inverse(inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
double_divide(multiply(inverse(inverse(inverse(X2))),X),identity) = double_divide(multiply(inverse(inverse(inverse(X2))),X),double_divide(X2,inverse(inverse(inverse(X2))))),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
double_divide(identity,double_divide(multiply(inverse(inverse(inverse(X2))),X),identity)) = double_divide(identity,double_divide(multiply(inverse(inverse(inverse(X2))),X),double_divide(X2,inverse(inverse(inverse(X2)))))),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(multiply(inverse(inverse(inverse(X2))),X),identity))) = double_divide(double_divide(identity,X),double_divide(identity,double_divide(multiply(inverse(inverse(inverse(X2))),X),double_divide(X2,inverse(inverse(inverse(X2))))))),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(multiply(inverse(inverse(inverse(X2))),X),double_divide(X2,inverse(inverse(inverse(X2))))))) = X2,
inference(substitution,[status(thm)],[c27]) ).
cnf(c138,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(multiply(inverse(inverse(inverse(X2))),X),identity))) = X2,
inference(transitivity,[status(thm)],[c136,c137]) ).
cnf(c139,plain,
double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(inverse(inverse(X2))),X)))) = X2,
inference(transitivity,[status(thm)],[c35,c138]) ).
cnf(c140,plain,
inverse(inverse(X)) = X,
inference(transitivity,[status(thm)],[c32,c139]) ).
cnf(c141,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c142,plain,
multiply(X2,X) = multiply(X2,inverse(inverse(X))),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
multiply(multiply(X3,X2),X) = multiply(multiply(X3,inverse(inverse(X2))),X),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c145,plain,
multiply(X2,inverse(X)) = multiply(inverse(inverse(X2)),inverse(X)),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
multiply(multiply(X3,inverse(X2)),X) = multiply(multiply(inverse(inverse(X3)),inverse(X2)),X),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c148,plain,
double_divide(identity,X) = double_divide(identity,inverse(inverse(X))),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
double_divide(identity,inverse(inverse(X))) = inverse(X),
inference(substitution,[status(thm)],[c121]) ).
cnf(c150,plain,
double_divide(identity,X) = inverse(X),
inference(transitivity,[status(thm)],[c148,c149]) ).
cnf(c151,plain,
inverse(X) = double_divide(identity,X),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
double_divide(X2,inverse(X)) = double_divide(X2,double_divide(identity,X)),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(X2),X)))) = X2,
inference(substitution,[status(thm)],[c30]) ).
cnf(c154,plain,
X2 = double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(X2),X)))),
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,plain,
double_divide(X2,double_divide(identity,X)) = double_divide(double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(X2),X)))),double_divide(identity,X)),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
multiply(double_divide(X,X2),identity) = double_divide(X,X2),
inference(substitution,[status(thm)],[c93]) ).
cnf(c157,plain,
double_divide(X,X2) = multiply(double_divide(X,X2),identity),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
double_divide(X2,double_divide(X,X2)) = double_divide(X2,multiply(double_divide(X,X2),identity)),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
inverse(double_divide(identity,double_divide(X,X2))) = multiply(double_divide(X,X2),identity),
inference(substitution,[status(thm)],[c15]) ).
cnf(c160,plain,
multiply(double_divide(X,X2),identity) = inverse(double_divide(identity,double_divide(X,X2))),
inference(symmetry,[status(thm)],[c159]) ).
cnf(c161,plain,
double_divide(X2,multiply(double_divide(X,X2),identity)) = double_divide(X2,inverse(double_divide(identity,double_divide(X,X2)))),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
double_divide(identity,double_divide(identity,double_divide(X,X2))) = inverse(double_divide(identity,double_divide(X,X2))),
inference(substitution,[status(thm)],[c150]) ).
cnf(c163,plain,
inverse(double_divide(identity,double_divide(X,X2))) = double_divide(identity,double_divide(identity,double_divide(X,X2))),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
double_divide(X2,inverse(double_divide(identity,double_divide(X,X2)))) = double_divide(X2,double_divide(identity,double_divide(identity,double_divide(X,X2)))),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
X = double_divide(identity,inverse(X)),
inference(symmetry,[status(thm)],[c121]) ).
cnf(c166,plain,
double_divide(X2,double_divide(identity,double_divide(identity,double_divide(X,X2)))) = double_divide(double_divide(identity,inverse(X2)),double_divide(identity,double_divide(identity,double_divide(X,X2)))),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c168,plain,
multiply(X,inverse(X)) = multiply(inverse(inverse(X)),inverse(X)),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
multiply(inverse(inverse(X)),inverse(X)) = inverse(identity),
inference(substitution,[status(thm)],[c55]) ).
cnf(c170,plain,
multiply(inverse(inverse(X)),inverse(X)) = identity,
inference(transitivity,[status(thm)],[c169,c82]) ).
cnf(c171,plain,
multiply(X,inverse(X)) = identity,
inference(transitivity,[status(thm)],[c168,c170]) ).
cnf(c172,plain,
identity = multiply(X,inverse(X)),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,plain,
double_divide(identity,double_divide(X,X2)) = double_divide(multiply(X2,inverse(X2)),double_divide(X,X2)),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
double_divide(identity,double_divide(identity,double_divide(X,X2))) = double_divide(identity,double_divide(multiply(X2,inverse(X2)),double_divide(X,X2))),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
double_divide(double_divide(identity,inverse(X2)),double_divide(identity,double_divide(identity,double_divide(X,X2)))) = double_divide(double_divide(identity,inverse(X2)),double_divide(identity,double_divide(multiply(X2,inverse(X2)),double_divide(X,X2)))),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
double_divide(double_divide(identity,inverse(X2)),double_divide(identity,double_divide(multiply(X2,inverse(X2)),double_divide(X,X2)))) = X,
inference(substitution,[status(thm)],[c27]) ).
cnf(c177,plain,
double_divide(double_divide(identity,inverse(X2)),double_divide(identity,double_divide(identity,double_divide(X,X2)))) = X,
inference(transitivity,[status(thm)],[c175,c176]) ).
cnf(c178,plain,
double_divide(X2,double_divide(identity,double_divide(identity,double_divide(X,X2)))) = X,
inference(transitivity,[status(thm)],[c166,c177]) ).
cnf(c179,plain,
double_divide(X2,inverse(double_divide(identity,double_divide(X,X2)))) = X,
inference(transitivity,[status(thm)],[c164,c178]) ).
cnf(c180,plain,
double_divide(X2,multiply(double_divide(X,X2),identity)) = X,
inference(transitivity,[status(thm)],[c161,c179]) ).
cnf(c181,plain,
double_divide(X2,double_divide(X,X2)) = X,
inference(transitivity,[status(thm)],[c158,c180]) ).
cnf(c182,plain,
double_divide(X,double_divide(X2,X)) = X2,
inference(substitution,[status(thm)],[c181]) ).
cnf(c183,plain,
X2 = double_divide(X,double_divide(X2,X)),
inference(symmetry,[status(thm)],[c182]) ).
cnf(c184,plain,
double_divide(double_divide(X2,X),X2) = double_divide(double_divide(X2,X),double_divide(X,double_divide(X2,X))),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
double_divide(double_divide(X2,X),double_divide(X,double_divide(X2,X))) = X,
inference(substitution,[status(thm)],[c181]) ).
cnf(c186,plain,
double_divide(double_divide(X2,X),X2) = X,
inference(transitivity,[status(thm)],[c184,c185]) ).
cnf(c187,plain,
double_divide(double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(X2),X)))),double_divide(identity,X)) = double_divide(identity,inverse(multiply(inverse(X2),X))),
inference(substitution,[status(thm)],[c186]) ).
cnf(c188,plain,
double_divide(identity,inverse(multiply(inverse(X2),X))) = multiply(inverse(X2),X),
inference(substitution,[status(thm)],[c121]) ).
cnf(c189,plain,
double_divide(double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(X2),X)))),double_divide(identity,X)) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c187,c188]) ).
cnf(c190,plain,
double_divide(X2,double_divide(identity,X)) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c155,c189]) ).
cnf(c191,plain,
double_divide(X2,inverse(X)) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c152,c190]) ).
cnf(c192,plain,
multiply(inverse(X2),X) = double_divide(X2,inverse(X)),
inference(symmetry,[status(thm)],[c191]) ).
cnf(c193,plain,
multiply(X2,multiply(inverse(X2),X)) = multiply(X2,double_divide(X2,inverse(X))),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c195,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c194]) ).
cnf(c196,plain,
inverse(multiply(X2,X)) = inverse(inverse(double_divide(X,X2))),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
inverse(inverse(double_divide(X,X2))) = double_divide(X,X2),
inference(substitution,[status(thm)],[c140]) ).
cnf(c198,plain,
inverse(multiply(X2,X)) = double_divide(X,X2),
inference(transitivity,[status(thm)],[c196,c197]) ).
cnf(c199,plain,
inverse(multiply(inverse(X),X2)) = double_divide(X2,inverse(X)),
inference(substitution,[status(thm)],[c198]) ).
cnf(c200,plain,
double_divide(X2,inverse(X)) = inverse(multiply(inverse(X),X2)),
inference(symmetry,[status(thm)],[c199]) ).
cnf(c201,plain,
multiply(X2,double_divide(X2,inverse(X))) = multiply(X2,inverse(multiply(inverse(X),X2))),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c203,plain,
multiply(X,inverse(X2)) = multiply(inverse(inverse(X)),inverse(X2)),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
double_divide(X2,multiply(X,inverse(X2))) = double_divide(X2,multiply(inverse(inverse(X)),inverse(X2))),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
double_divide(X2,multiply(inverse(inverse(X)),inverse(X2))) = inverse(X),
inference(substitution,[status(thm)],[c129]) ).
cnf(c206,plain,
double_divide(X2,multiply(X,inverse(X2))) = inverse(X),
inference(transitivity,[status(thm)],[c204,c205]) ).
cnf(c207,plain,
double_divide(X,multiply(X2,inverse(X))) = inverse(X2),
inference(substitution,[status(thm)],[c206]) ).
cnf(c208,plain,
inverse(X2) = double_divide(X,multiply(X2,inverse(X))),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,plain,
double_divide(inverse(X2),X) = double_divide(double_divide(X,multiply(X2,inverse(X))),X),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
double_divide(double_divide(X,multiply(X2,inverse(X))),X) = multiply(X2,inverse(X)),
inference(substitution,[status(thm)],[c186]) ).
cnf(c211,plain,
double_divide(inverse(X2),X) = multiply(X2,inverse(X)),
inference(transitivity,[status(thm)],[c209,c210]) ).
cnf(c212,plain,
double_divide(inverse(X2),multiply(inverse(X),X2)) = multiply(X2,inverse(multiply(inverse(X),X2))),
inference(substitution,[status(thm)],[c211]) ).
cnf(c213,plain,
multiply(X2,inverse(multiply(inverse(X),X2))) = double_divide(inverse(X2),multiply(inverse(X),X2)),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c214,plain,
inverse(X) = double_divide(identity,X),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c215,plain,
double_divide(inverse(X2),multiply(inverse(X),X2)) = double_divide(double_divide(identity,X2),multiply(inverse(X),X2)),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
double_divide(identity,inverse(multiply(inverse(X),X2))) = multiply(inverse(X),X2),
inference(substitution,[status(thm)],[c121]) ).
cnf(c217,plain,
multiply(inverse(X),X2) = double_divide(identity,inverse(multiply(inverse(X),X2))),
inference(symmetry,[status(thm)],[c216]) ).
cnf(c218,plain,
double_divide(double_divide(identity,X2),multiply(inverse(X),X2)) = double_divide(double_divide(identity,X2),double_divide(identity,inverse(multiply(inverse(X),X2)))),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
double_divide(double_divide(identity,X2),multiply(inverse(X),X2)) = X,
inference(transitivity,[status(thm)],[c218,c30]) ).
cnf(c220,plain,
double_divide(inverse(X2),multiply(inverse(X),X2)) = X,
inference(transitivity,[status(thm)],[c215,c219]) ).
cnf(c221,plain,
multiply(X2,inverse(multiply(inverse(X),X2))) = X,
inference(transitivity,[status(thm)],[c213,c220]) ).
cnf(c222,plain,
multiply(X2,double_divide(X2,inverse(X))) = X,
inference(transitivity,[status(thm)],[c201,c221]) ).
cnf(c223,plain,
multiply(X2,multiply(inverse(X2),X)) = X,
inference(transitivity,[status(thm)],[c193,c222]) ).
cnf(c224,plain,
multiply(X3,multiply(inverse(X3),multiply(multiply(inverse(inverse(X3)),inverse(X2)),X))) = multiply(multiply(inverse(inverse(X3)),inverse(X2)),X),
inference(substitution,[status(thm)],[c223]) ).
cnf(c225,plain,
multiply(multiply(inverse(inverse(X3)),inverse(X2)),X) = multiply(X3,multiply(inverse(X3),multiply(multiply(inverse(inverse(X3)),inverse(X2)),X))),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c226,plain,
multiply(inverse(X),multiply(inverse(inverse(X)),X2)) = X2,
inference(substitution,[status(thm)],[c223]) ).
cnf(c227,plain,
X2 = multiply(inverse(X),multiply(inverse(inverse(X)),X2)),
inference(symmetry,[status(thm)],[c226]) ).
cnf(c228,plain,
double_divide(X2,X) = double_divide(multiply(inverse(X),multiply(inverse(inverse(X)),X2)),X),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c230,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c229]) ).
cnf(c231,plain,
double_divide(identity,multiply(X2,X)) = double_divide(identity,inverse(double_divide(X,X2))),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
double_divide(identity,inverse(double_divide(X,X2))) = double_divide(X,X2),
inference(substitution,[status(thm)],[c121]) ).
cnf(c233,plain,
double_divide(identity,multiply(X2,X)) = double_divide(X,X2),
inference(transitivity,[status(thm)],[c231,c232]) ).
cnf(c234,plain,
double_divide(identity,multiply(X2,multiply(inverse(X2),X))) = double_divide(multiply(inverse(X2),X),X2),
inference(substitution,[status(thm)],[c233]) ).
cnf(c235,plain,
double_divide(multiply(inverse(X2),X),X2) = double_divide(identity,multiply(X2,multiply(inverse(X2),X))),
inference(symmetry,[status(thm)],[c234]) ).
cnf(c236,plain,
double_divide(identity,multiply(X2,multiply(inverse(X2),X))) = double_divide(identity,X),
inference(congruence,[status(thm)],[c223]) ).
cnf(c237,plain,
double_divide(identity,multiply(X2,multiply(inverse(X2),X))) = inverse(X),
inference(transitivity,[status(thm)],[c236,c150]) ).
cnf(c238,plain,
double_divide(multiply(inverse(X2),X),X2) = inverse(X),
inference(transitivity,[status(thm)],[c235,c237]) ).
cnf(c239,plain,
double_divide(multiply(inverse(X),multiply(inverse(inverse(X)),X2)),X) = inverse(multiply(inverse(inverse(X)),X2)),
inference(substitution,[status(thm)],[c238]) ).
cnf(c240,plain,
inverse(multiply(inverse(inverse(X)),X2)) = double_divide(X2,inverse(inverse(X))),
inference(substitution,[status(thm)],[c198]) ).
cnf(c241,plain,
double_divide(X2,inverse(inverse(X))) = multiply(inverse(X2),inverse(X)),
inference(substitution,[status(thm)],[c191]) ).
cnf(c242,plain,
inverse(multiply(inverse(inverse(X)),X2)) = multiply(inverse(X2),inverse(X)),
inference(transitivity,[status(thm)],[c240,c241]) ).
cnf(c243,plain,
double_divide(multiply(inverse(X),multiply(inverse(inverse(X)),X2)),X) = multiply(inverse(X2),inverse(X)),
inference(transitivity,[status(thm)],[c239,c242]) ).
cnf(c244,plain,
double_divide(X2,X) = multiply(inverse(X2),inverse(X)),
inference(transitivity,[status(thm)],[c228,c243]) ).
cnf(c245,plain,
multiply(inverse(X2),inverse(X)) = double_divide(X2,X),
inference(symmetry,[status(thm)],[c244]) ).
cnf(c246,plain,
multiply(multiply(inverse(X3),inverse(X2)),X) = multiply(double_divide(X3,X2),X),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
multiply(X3,multiply(multiply(inverse(X3),inverse(X2)),X)) = multiply(X3,multiply(double_divide(X3,X2),X)),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,plain,
inverse(multiply(X,X2)) = double_divide(X2,X),
inference(substitution,[status(thm)],[c198]) ).
cnf(c249,plain,
double_divide(X2,X) = inverse(multiply(X,X2)),
inference(symmetry,[status(thm)],[c248]) ).
cnf(c250,plain,
multiply(double_divide(X3,X2),X) = multiply(inverse(multiply(X2,X3)),X),
inference(congruence,[status(thm)],[c249]) ).
cnf(c251,plain,
multiply(X3,multiply(double_divide(X3,X2),X)) = multiply(X3,multiply(inverse(multiply(X2,X3)),X)),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
double_divide(multiply(X2,X3),inverse(X)) = multiply(inverse(multiply(X2,X3)),X),
inference(substitution,[status(thm)],[c191]) ).
cnf(c253,plain,
multiply(inverse(multiply(X2,X3)),X) = double_divide(multiply(X2,X3),inverse(X)),
inference(symmetry,[status(thm)],[c252]) ).
cnf(c254,plain,
multiply(X3,multiply(inverse(multiply(X2,X3)),X)) = multiply(X3,double_divide(multiply(X2,X3),inverse(X))),
inference(congruence,[status(thm)],[c253]) ).
cnf(c255,plain,
multiply(double_divide(multiply(X2,X3),inverse(X)),identity) = double_divide(multiply(X2,X3),inverse(X)),
inference(substitution,[status(thm)],[c93]) ).
cnf(c256,plain,
double_divide(multiply(X2,X3),inverse(X)) = multiply(double_divide(multiply(X2,X3),inverse(X)),identity),
inference(symmetry,[status(thm)],[c255]) ).
cnf(c257,plain,
multiply(X3,double_divide(multiply(X2,X3),inverse(X))) = multiply(X3,multiply(double_divide(multiply(X2,X3),inverse(X)),identity)),
inference(congruence,[status(thm)],[c256]) ).
cnf(c258,plain,
inverse(double_divide(identity,double_divide(multiply(X2,X3),inverse(X)))) = multiply(double_divide(multiply(X2,X3),inverse(X)),identity),
inference(substitution,[status(thm)],[c15]) ).
cnf(c259,plain,
multiply(double_divide(multiply(X2,X3),inverse(X)),identity) = inverse(double_divide(identity,double_divide(multiply(X2,X3),inverse(X)))),
inference(symmetry,[status(thm)],[c258]) ).
cnf(c260,plain,
multiply(X3,multiply(double_divide(multiply(X2,X3),inverse(X)),identity)) = multiply(X3,inverse(double_divide(identity,double_divide(multiply(X2,X3),inverse(X))))),
inference(congruence,[status(thm)],[c259]) ).
cnf(c261,plain,
X = multiply(X,identity),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c262,plain,
multiply(X3,inverse(double_divide(identity,double_divide(multiply(X2,X3),inverse(X))))) = multiply(multiply(X3,identity),inverse(double_divide(identity,double_divide(multiply(X2,X3),inverse(X))))),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
inverse(double_divide(identity,X)) = multiply(X,identity),
inference(substitution,[status(thm)],[c15]) ).
cnf(c264,plain,
multiply(X,identity) = inverse(double_divide(identity,X)),
inference(symmetry,[status(thm)],[c263]) ).
cnf(c265,plain,
multiply(multiply(X3,identity),inverse(double_divide(identity,double_divide(multiply(X2,X3),inverse(X))))) = multiply(inverse(double_divide(identity,X3)),inverse(double_divide(identity,double_divide(multiply(X2,X3),inverse(X))))),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
double_divide(double_divide(identity,X3),double_divide(identity,double_divide(multiply(X2,X3),inverse(X)))) = multiply(inverse(double_divide(identity,X3)),inverse(double_divide(identity,double_divide(multiply(X2,X3),inverse(X))))),
inference(substitution,[status(thm)],[c244]) ).
cnf(c267,plain,
multiply(inverse(double_divide(identity,X3)),inverse(double_divide(identity,double_divide(multiply(X2,X3),inverse(X))))) = double_divide(double_divide(identity,X3),double_divide(identity,double_divide(multiply(X2,X3),inverse(X)))),
inference(symmetry,[status(thm)],[c266]) ).
cnf(c268,plain,
inverse(X) = double_divide(multiply(inverse(X2),X),X2),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c269,plain,
double_divide(multiply(X2,X3),inverse(X)) = double_divide(multiply(X2,X3),double_divide(multiply(inverse(X2),X),X2)),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
double_divide(identity,double_divide(multiply(X2,X3),inverse(X))) = double_divide(identity,double_divide(multiply(X2,X3),double_divide(multiply(inverse(X2),X),X2))),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
double_divide(double_divide(identity,X3),double_divide(identity,double_divide(multiply(X2,X3),inverse(X)))) = double_divide(double_divide(identity,X3),double_divide(identity,double_divide(multiply(X2,X3),double_divide(multiply(inverse(X2),X),X2)))),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
double_divide(double_divide(identity,X3),double_divide(identity,double_divide(multiply(X2,X3),double_divide(multiply(inverse(X2),X),X2)))) = multiply(inverse(X2),X),
inference(substitution,[status(thm)],[c27]) ).
cnf(c273,plain,
double_divide(double_divide(identity,X3),double_divide(identity,double_divide(multiply(X2,X3),inverse(X)))) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c271,c272]) ).
cnf(c274,plain,
multiply(inverse(double_divide(identity,X3)),inverse(double_divide(identity,double_divide(multiply(X2,X3),inverse(X))))) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c267,c273]) ).
cnf(c275,plain,
multiply(multiply(X3,identity),inverse(double_divide(identity,double_divide(multiply(X2,X3),inverse(X))))) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c265,c274]) ).
cnf(c276,plain,
multiply(X3,inverse(double_divide(identity,double_divide(multiply(X2,X3),inverse(X))))) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c262,c275]) ).
cnf(c277,plain,
multiply(X3,multiply(double_divide(multiply(X2,X3),inverse(X)),identity)) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c260,c276]) ).
cnf(c278,plain,
multiply(X3,double_divide(multiply(X2,X3),inverse(X))) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c257,c277]) ).
cnf(c279,plain,
multiply(X3,multiply(inverse(multiply(X2,X3)),X)) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c254,c278]) ).
cnf(c280,plain,
multiply(X3,multiply(double_divide(X3,X2),X)) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c251,c279]) ).
cnf(c281,plain,
multiply(X3,multiply(multiply(inverse(X3),inverse(X2)),X)) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c247,c280]) ).
cnf(c282,plain,
multiply(inverse(X3),multiply(multiply(inverse(inverse(X3)),inverse(X2)),X)) = multiply(inverse(X2),X),
inference(substitution,[status(thm)],[c281]) ).
cnf(c283,plain,
multiply(X3,multiply(inverse(X3),multiply(multiply(inverse(inverse(X3)),inverse(X2)),X))) = multiply(X3,multiply(inverse(X2),X)),
inference(congruence,[status(thm)],[c282]) ).
cnf(c284,plain,
multiply(multiply(inverse(inverse(X3)),inverse(X2)),X) = multiply(X3,multiply(inverse(X2),X)),
inference(transitivity,[status(thm)],[c225,c283]) ).
cnf(c285,plain,
multiply(multiply(X3,inverse(X2)),X) = multiply(X3,multiply(inverse(X2),X)),
inference(transitivity,[status(thm)],[c146,c284]) ).
cnf(c286,plain,
multiply(multiply(X3,inverse(inverse(X2))),X) = multiply(X3,multiply(inverse(inverse(X2)),X)),
inference(substitution,[status(thm)],[c285]) ).
cnf(c287,plain,
multiply(inverse(inverse(X2)),X) = multiply(X2,X),
inference(congruence,[status(thm)],[c140]) ).
cnf(c288,plain,
multiply(X3,multiply(inverse(inverse(X2)),X)) = multiply(X3,multiply(X2,X)),
inference(congruence,[status(thm)],[c287]) ).
cnf(c289,plain,
multiply(multiply(X3,inverse(inverse(X2))),X) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c286,c288]) ).
cnf(c290,plain,
multiply(multiply(X3,X2),X) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c143,c289]) ).
cnf(c291,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(substitution,[status(thm)],[c290]) ).
cnf(c292,plain,
$false,
inference(resolution,[status(thm)],[c1,c291]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP492-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 10:06:03 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.45 Command-line arguments: --no-flatten-goal
% 0.13/0.45
% 0.13/0.45 % SZS status Unsatisfiable
% 0.13/0.45
% 0.13/0.48 % SZS output start CNFRefutation
% See solution above
% 1.19/0.61
% 1.19/0.61 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------