%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP575-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 0.32s 0.55s
% Output : CNFRefutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 93
% Number of leaves : 5
% Syntax : Number of clauses : 347 ( 347 unt; 0 nHn; 36 RR)
% Number of literals : 347 ( 346 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 : 587 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(c2,axiom,
inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(multiply(a3,b3),c3) = multiply(c3,multiply(a3,b3)),
inference(substitution,[status(thm)],[c179]) ).
cnf(c181,plain,
multiply(X,X2) = multiply(X2,X),
inference(substitution,[status(thm)],[c179]) ).
cnf(c182,plain,
multiply(X2,X) = multiply(X,X2),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
multiply(X2,multiply(X3,X)) = multiply(X2,multiply(X,X3)),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
inverse(double_divide(X,double_divide(inverse(X2),X))) = multiply(double_divide(inverse(X2),X),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c185,plain,
multiply(double_divide(inverse(X2),X),X) = inverse(double_divide(X,double_divide(inverse(X2),X))),
inference(symmetry,[status(thm)],[c184]) ).
cnf(c186,plain,
inverse(double_divide(X,double_divide(inverse(X2),X))) = double_divide(double_divide(X,double_divide(inverse(X2),X)),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c187,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c188,plain,
double_divide(double_divide(X,double_divide(inverse(X2),X)),identity) = double_divide(double_divide(X,double_divide(inverse(X2),X)),inverse(identity)),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
X = inverse(inverse(inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c190,plain,
double_divide(inverse(X2),X) = double_divide(inverse(X2),inverse(inverse(inverse(inverse(X))))),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
double_divide(X,double_divide(inverse(X2),X)) = double_divide(X,double_divide(inverse(X2),inverse(inverse(inverse(inverse(X)))))),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
double_divide(double_divide(X,double_divide(inverse(X2),X)),inverse(identity)) = double_divide(double_divide(X,double_divide(inverse(X2),inverse(inverse(inverse(inverse(X)))))),inverse(identity)),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
X = inverse(inverse(inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c194,plain,
double_divide(X,double_divide(inverse(X2),inverse(inverse(inverse(inverse(X)))))) = double_divide(inverse(inverse(inverse(inverse(X)))),double_divide(inverse(X2),inverse(inverse(inverse(inverse(X)))))),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
double_divide(double_divide(X,double_divide(inverse(X2),inverse(inverse(inverse(inverse(X)))))),inverse(identity)) = double_divide(double_divide(inverse(inverse(inverse(inverse(X)))),double_divide(inverse(X2),inverse(inverse(inverse(inverse(X)))))),inverse(identity)),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
double_divide(double_divide(inverse(inverse(inverse(inverse(X)))),double_divide(inverse(X2),inverse(inverse(inverse(inverse(X)))))),inverse(identity)) = X2,
inference(substitution,[status(thm)],[c46]) ).
cnf(c197,plain,
double_divide(double_divide(X,double_divide(inverse(X2),inverse(inverse(inverse(inverse(X)))))),inverse(identity)) = X2,
inference(transitivity,[status(thm)],[c195,c196]) ).
cnf(c198,plain,
double_divide(double_divide(X,double_divide(inverse(X2),X)),inverse(identity)) = X2,
inference(transitivity,[status(thm)],[c192,c197]) ).
cnf(c199,plain,
double_divide(double_divide(X,double_divide(inverse(X2),X)),identity) = X2,
inference(transitivity,[status(thm)],[c188,c198]) ).
cnf(c200,plain,
inverse(double_divide(X,double_divide(inverse(X2),X))) = X2,
inference(transitivity,[status(thm)],[c186,c199]) ).
cnf(c201,plain,
multiply(double_divide(inverse(X2),X),X) = X2,
inference(transitivity,[status(thm)],[c185,c200]) ).
cnf(c202,plain,
multiply(double_divide(inverse(X3),multiply(inverse(X2),inverse(X))),multiply(inverse(X2),inverse(X))) = X3,
inference(substitution,[status(thm)],[c201]) ).
cnf(c203,plain,
X3 = multiply(double_divide(inverse(X3),multiply(inverse(X2),inverse(X))),multiply(inverse(X2),inverse(X))),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c204,plain,
multiply(X,X3) = multiply(X,multiply(double_divide(inverse(X3),multiply(inverse(X2),inverse(X))),multiply(inverse(X2),inverse(X)))),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
multiply(X2,multiply(X,X3)) = multiply(X2,multiply(X,multiply(double_divide(inverse(X3),multiply(inverse(X2),inverse(X))),multiply(inverse(X2),inverse(X))))),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
multiply(inverse(X),inverse(X2)) = multiply(inverse(X2),inverse(X)),
inference(substitution,[status(thm)],[c179]) ).
cnf(c207,plain,
multiply(inverse(X2),inverse(X)) = multiply(inverse(X),inverse(X2)),
inference(symmetry,[status(thm)],[c206]) ).
cnf(c208,plain,
multiply(X,multiply(inverse(X3),inverse(X2))) = multiply(X,multiply(inverse(X2),inverse(X3))),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
multiply(X2,multiply(X,multiply(inverse(X3),inverse(X2)))) = multiply(X2,multiply(X,multiply(inverse(X2),inverse(X3)))),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
multiply(X3,multiply(X2,multiply(X,multiply(inverse(X3),inverse(X2))))) = multiply(X3,multiply(X2,multiply(X,multiply(inverse(X2),inverse(X3))))),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
multiply(double_divide(inverse(X),inverse(X2)),inverse(X2)) = X,
inference(substitution,[status(thm)],[c201]) ).
cnf(c212,plain,
X = multiply(double_divide(inverse(X),inverse(X2)),inverse(X2)),
inference(symmetry,[status(thm)],[c211]) ).
cnf(c213,plain,
double_divide(X2,X) = double_divide(X2,multiply(double_divide(inverse(X),inverse(X2)),inverse(X2))),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
multiply(inverse(X2),X) = multiply(X,inverse(X2)),
inference(substitution,[status(thm)],[c179]) ).
cnf(c215,plain,
multiply(X,inverse(X2)) = multiply(inverse(X2),X),
inference(symmetry,[status(thm)],[c214]) ).
cnf(c216,plain,
double_divide(X2,multiply(X,inverse(X2))) = double_divide(X2,multiply(inverse(X2),X)),
inference(congruence,[status(thm)],[c215]) ).
cnf(c217,plain,
inverse(inverse(inverse(multiply(multiply(inverse(X2),X),X2)))) = double_divide(X2,multiply(inverse(X2),X)),
inference(substitution,[status(thm)],[c108]) ).
cnf(c218,plain,
double_divide(X2,multiply(inverse(X2),X)) = inverse(inverse(inverse(multiply(multiply(inverse(X2),X),X2)))),
inference(symmetry,[status(thm)],[c217]) ).
cnf(c219,plain,
inverse(multiply(multiply(inverse(X2),X),X2)) = inverse(X),
inference(congruence,[status(thm)],[c151]) ).
cnf(c220,plain,
inverse(inverse(multiply(multiply(inverse(X2),X),X2))) = inverse(inverse(X)),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
inverse(inverse(inverse(multiply(multiply(inverse(X2),X),X2)))) = inverse(inverse(inverse(X))),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
inverse(inverse(inverse(X))) = inverse(X),
inference(substitution,[status(thm)],[c155]) ).
cnf(c223,plain,
inverse(inverse(inverse(multiply(multiply(inverse(X2),X),X2)))) = inverse(X),
inference(transitivity,[status(thm)],[c221,c222]) ).
cnf(c224,plain,
double_divide(X2,multiply(inverse(X2),X)) = inverse(X),
inference(transitivity,[status(thm)],[c218,c223]) ).
cnf(c225,plain,
double_divide(X2,multiply(X,inverse(X2))) = inverse(X),
inference(transitivity,[status(thm)],[c216,c224]) ).
cnf(c226,plain,
double_divide(X2,multiply(double_divide(inverse(X),inverse(X2)),inverse(X2))) = inverse(double_divide(inverse(X),inverse(X2))),
inference(substitution,[status(thm)],[c225]) ).
cnf(c227,plain,
inverse(inverse(double_divide(X,X2))) = double_divide(X,X2),
inference(substitution,[status(thm)],[c155]) ).
cnf(c228,plain,
double_divide(X,X2) = inverse(inverse(double_divide(X,X2))),
inference(symmetry,[status(thm)],[c227]) ).
cnf(c229,plain,
multiply(X,X2) = multiply(X2,X),
inference(substitution,[status(thm)],[c179]) ).
cnf(c230,plain,
multiply(X2,X) = multiply(X,X2),
inference(symmetry,[status(thm)],[c229]) ).
cnf(c231,plain,
inverse(multiply(X2,X)) = inverse(multiply(X,X2)),
inference(congruence,[status(thm)],[c230]) ).
cnf(c232,plain,
multiply(X,X2) = inverse(double_divide(X2,X)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c233,plain,
inverse(multiply(X,X2)) = inverse(inverse(double_divide(X2,X))),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
inverse(inverse(double_divide(X2,X))) = double_divide(X2,X),
inference(substitution,[status(thm)],[c155]) ).
cnf(c235,plain,
inverse(multiply(X,X2)) = double_divide(X2,X),
inference(transitivity,[status(thm)],[c233,c234]) ).
cnf(c236,plain,
inverse(multiply(X2,X)) = double_divide(X2,X),
inference(transitivity,[status(thm)],[c231,c235]) ).
cnf(c237,plain,
inverse(multiply(X,X2)) = double_divide(X,X2),
inference(substitution,[status(thm)],[c236]) ).
cnf(c238,plain,
double_divide(X,X2) = inverse(multiply(X,X2)),
inference(symmetry,[status(thm)],[c237]) ).
cnf(c239,plain,
inverse(double_divide(X,X2)) = inverse(inverse(multiply(X,X2))),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
inverse(inverse(double_divide(X,X2))) = inverse(inverse(inverse(multiply(X,X2)))),
inference(congruence,[status(thm)],[c239]) ).
cnf(c241,plain,
inverse(inverse(inverse(multiply(X,X2)))) = double_divide(X2,X),
inference(substitution,[status(thm)],[c108]) ).
cnf(c242,plain,
inverse(inverse(double_divide(X,X2))) = double_divide(X2,X),
inference(transitivity,[status(thm)],[c240,c241]) ).
cnf(c243,plain,
double_divide(X,X2) = double_divide(X2,X),
inference(transitivity,[status(thm)],[c228,c242]) ).
cnf(c244,plain,
double_divide(X2,X) = double_divide(X,X2),
inference(substitution,[status(thm)],[c243]) ).
cnf(c245,plain,
inverse(double_divide(X2,X)) = inverse(double_divide(X,X2)),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
inverse(multiply(X,X2)) = double_divide(X,X2),
inference(substitution,[status(thm)],[c236]) ).
cnf(c247,plain,
double_divide(X,X2) = inverse(multiply(X,X2)),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
inverse(double_divide(X,X2)) = inverse(inverse(multiply(X,X2))),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
inverse(inverse(multiply(X,X2))) = multiply(X,X2),
inference(substitution,[status(thm)],[c155]) ).
cnf(c250,plain,
multiply(X,X2) = multiply(X2,X),
inference(substitution,[status(thm)],[c179]) ).
cnf(c251,plain,
inverse(inverse(multiply(X,X2))) = multiply(X2,X),
inference(transitivity,[status(thm)],[c249,c250]) ).
cnf(c252,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c248,c251]) ).
cnf(c253,plain,
inverse(double_divide(X2,X)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c245,c252]) ).
cnf(c254,plain,
inverse(double_divide(inverse(X),inverse(X2))) = multiply(inverse(X),inverse(X2)),
inference(substitution,[status(thm)],[c253]) ).
cnf(c255,plain,
multiply(inverse(X),inverse(X2)) = multiply(inverse(X2),inverse(X)),
inference(substitution,[status(thm)],[c179]) ).
cnf(c256,plain,
inverse(double_divide(inverse(X),inverse(X2))) = multiply(inverse(X2),inverse(X)),
inference(transitivity,[status(thm)],[c254,c255]) ).
cnf(c257,plain,
double_divide(X2,multiply(double_divide(inverse(X),inverse(X2)),inverse(X2))) = multiply(inverse(X2),inverse(X)),
inference(transitivity,[status(thm)],[c226,c256]) ).
cnf(c258,plain,
double_divide(X2,X) = multiply(inverse(X2),inverse(X)),
inference(transitivity,[status(thm)],[c213,c257]) ).
cnf(c259,plain,
double_divide(X,X2) = multiply(inverse(X),inverse(X2)),
inference(substitution,[status(thm)],[c258]) ).
cnf(c260,plain,
multiply(inverse(X),inverse(X2)) = double_divide(X,X2),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c261,plain,
multiply(X,multiply(inverse(X2),inverse(X3))) = multiply(X,double_divide(X2,X3)),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
multiply(X2,multiply(X,multiply(inverse(X2),inverse(X3)))) = multiply(X2,multiply(X,double_divide(X2,X3))),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
multiply(X3,multiply(X2,multiply(X,multiply(inverse(X2),inverse(X3))))) = multiply(X3,multiply(X2,multiply(X,double_divide(X2,X3)))),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
inverse(double_divide(X,double_divide(X2,X3))) = multiply(X,double_divide(X2,X3)),
inference(substitution,[status(thm)],[c253]) ).
cnf(c265,plain,
multiply(X,double_divide(X2,X3)) = inverse(double_divide(X,double_divide(X2,X3))),
inference(symmetry,[status(thm)],[c264]) ).
cnf(c266,plain,
multiply(X2,multiply(X,double_divide(X2,X3))) = multiply(X2,inverse(double_divide(X,double_divide(X2,X3)))),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,plain,
multiply(X3,multiply(X2,multiply(X,double_divide(X2,X3)))) = multiply(X3,multiply(X2,inverse(double_divide(X,double_divide(X2,X3))))),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
inverse(double_divide(X,inverse(X2))) = multiply(X,inverse(X2)),
inference(substitution,[status(thm)],[c253]) ).
cnf(c269,plain,
multiply(X,inverse(X2)) = inverse(double_divide(X,inverse(X2))),
inference(symmetry,[status(thm)],[c268]) ).
cnf(c270,plain,
multiply(X2,multiply(X,inverse(X2))) = multiply(X2,inverse(double_divide(X,inverse(X2)))),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
inverse(double_divide(X,inverse(X2))) = double_divide(double_divide(X,inverse(X2)),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c272,plain,
multiply(X2,inverse(double_divide(X,inverse(X2)))) = multiply(X2,double_divide(double_divide(X,inverse(X2)),identity)),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
inverse(double_divide(X2,double_divide(double_divide(X,inverse(X2)),identity))) = multiply(X2,double_divide(double_divide(X,inverse(X2)),identity)),
inference(substitution,[status(thm)],[c253]) ).
cnf(c274,plain,
multiply(X2,double_divide(double_divide(X,inverse(X2)),identity)) = inverse(double_divide(X2,double_divide(double_divide(X,inverse(X2)),identity))),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
inverse(double_divide(X2,double_divide(double_divide(X,inverse(X2)),identity))) = double_divide(double_divide(X2,double_divide(double_divide(X,inverse(X2)),identity)),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c276,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c277,plain,
double_divide(double_divide(X,inverse(X2)),identity) = double_divide(double_divide(X,inverse(X2)),inverse(identity)),
inference(congruence,[status(thm)],[c276]) ).
cnf(c278,plain,
double_divide(X2,double_divide(double_divide(X,inverse(X2)),identity)) = double_divide(X2,double_divide(double_divide(X,inverse(X2)),inverse(identity))),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
double_divide(double_divide(X2,double_divide(double_divide(X,inverse(X2)),identity)),identity) = double_divide(double_divide(X2,double_divide(double_divide(X,inverse(X2)),inverse(identity))),identity),
inference(congruence,[status(thm)],[c278]) ).
cnf(c280,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c281,plain,
double_divide(double_divide(X2,double_divide(double_divide(X,inverse(X2)),inverse(identity))),identity) = double_divide(double_divide(X2,double_divide(double_divide(X,inverse(X2)),inverse(identity))),inverse(identity)),
inference(congruence,[status(thm)],[c280]) ).
cnf(c282,plain,
inverse(X) = double_divide(identity,X),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c283,plain,
double_divide(X,inverse(X2)) = double_divide(X,double_divide(identity,X2)),
inference(congruence,[status(thm)],[c282]) ).
cnf(c284,plain,
double_divide(double_divide(X,inverse(X2)),inverse(identity)) = double_divide(double_divide(X,double_divide(identity,X2)),inverse(identity)),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
double_divide(X2,double_divide(double_divide(X,inverse(X2)),inverse(identity))) = double_divide(X2,double_divide(double_divide(X,double_divide(identity,X2)),inverse(identity))),
inference(congruence,[status(thm)],[c284]) ).
cnf(c286,plain,
double_divide(double_divide(X2,double_divide(double_divide(X,inverse(X2)),inverse(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)],[c285]) ).
cnf(c287,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(c288,plain,
double_divide(double_divide(X2,double_divide(double_divide(X,inverse(X2)),inverse(identity))),inverse(identity)) = X,
inference(transitivity,[status(thm)],[c286,c287]) ).
cnf(c289,plain,
double_divide(double_divide(X2,double_divide(double_divide(X,inverse(X2)),inverse(identity))),identity) = X,
inference(transitivity,[status(thm)],[c281,c288]) ).
cnf(c290,plain,
double_divide(double_divide(X2,double_divide(double_divide(X,inverse(X2)),identity)),identity) = X,
inference(transitivity,[status(thm)],[c279,c289]) ).
cnf(c291,plain,
inverse(double_divide(X2,double_divide(double_divide(X,inverse(X2)),identity))) = X,
inference(transitivity,[status(thm)],[c275,c290]) ).
cnf(c292,plain,
multiply(X2,double_divide(double_divide(X,inverse(X2)),identity)) = X,
inference(transitivity,[status(thm)],[c274,c291]) ).
cnf(c293,plain,
multiply(X2,inverse(double_divide(X,inverse(X2)))) = X,
inference(transitivity,[status(thm)],[c272,c292]) ).
cnf(c294,plain,
multiply(X2,multiply(X,inverse(X2))) = X,
inference(transitivity,[status(thm)],[c270,c293]) ).
cnf(c295,plain,
multiply(X,multiply(double_divide(X2,inverse(X)),inverse(X))) = double_divide(X2,inverse(X)),
inference(substitution,[status(thm)],[c294]) ).
cnf(c296,plain,
double_divide(X2,inverse(X)) = multiply(X,multiply(double_divide(X2,inverse(X)),inverse(X))),
inference(symmetry,[status(thm)],[c295]) ).
cnf(c297,plain,
X = inverse(inverse(inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c298,plain,
double_divide(X2,X) = double_divide(inverse(inverse(inverse(inverse(X2)))),X),
inference(congruence,[status(thm)],[c297]) ).
cnf(c299,plain,
multiply(double_divide(X2,X),X) = multiply(double_divide(inverse(inverse(inverse(inverse(X2)))),X),X),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
multiply(double_divide(inverse(inverse(inverse(inverse(X2)))),X),X) = inverse(inverse(inverse(X2))),
inference(substitution,[status(thm)],[c201]) ).
cnf(c301,plain,
multiply(double_divide(X2,X),X) = inverse(inverse(inverse(X2))),
inference(transitivity,[status(thm)],[c299,c300]) ).
cnf(c302,plain,
multiply(double_divide(X2,inverse(X)),inverse(X)) = inverse(inverse(inverse(X2))),
inference(substitution,[status(thm)],[c301]) ).
cnf(c303,plain,
multiply(X,multiply(double_divide(X2,inverse(X)),inverse(X))) = multiply(X,inverse(inverse(inverse(X2)))),
inference(congruence,[status(thm)],[c302]) ).
cnf(c304,plain,
inverse(inverse(inverse(X))) = inverse(X),
inference(substitution,[status(thm)],[c155]) ).
cnf(c305,plain,
multiply(X,inverse(inverse(inverse(X2)))) = multiply(X,inverse(X2)),
inference(congruence,[status(thm)],[c304]) ).
cnf(c306,plain,
multiply(X,multiply(double_divide(X2,inverse(X)),inverse(X))) = multiply(X,inverse(X2)),
inference(transitivity,[status(thm)],[c303,c305]) ).
cnf(c307,plain,
double_divide(X2,inverse(X)) = multiply(X,inverse(X2)),
inference(transitivity,[status(thm)],[c296,c306]) ).
cnf(c308,plain,
double_divide(double_divide(X,double_divide(X2,X3)),inverse(X2)) = multiply(X2,inverse(double_divide(X,double_divide(X2,X3)))),
inference(substitution,[status(thm)],[c307]) ).
cnf(c309,plain,
multiply(X2,inverse(double_divide(X,double_divide(X2,X3)))) = double_divide(double_divide(X,double_divide(X2,X3)),inverse(X2)),
inference(symmetry,[status(thm)],[c308]) ).
cnf(c310,plain,
multiply(X3,multiply(X2,inverse(double_divide(X,double_divide(X2,X3))))) = multiply(X3,double_divide(double_divide(X,double_divide(X2,X3)),inverse(X2))),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
inverse(double_divide(X3,double_divide(double_divide(X,double_divide(X2,X3)),inverse(X2)))) = multiply(X3,double_divide(double_divide(X,double_divide(X2,X3)),inverse(X2))),
inference(substitution,[status(thm)],[c253]) ).
cnf(c312,plain,
multiply(X3,double_divide(double_divide(X,double_divide(X2,X3)),inverse(X2))) = inverse(double_divide(X3,double_divide(double_divide(X,double_divide(X2,X3)),inverse(X2)))),
inference(symmetry,[status(thm)],[c311]) ).
cnf(c313,plain,
inverse(double_divide(X3,double_divide(double_divide(X,double_divide(X2,X3)),inverse(X2)))) = double_divide(double_divide(X3,double_divide(double_divide(X,double_divide(X2,X3)),inverse(X2))),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c314,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c315,plain,
double_divide(double_divide(X3,double_divide(double_divide(X,double_divide(X2,X3)),inverse(X2))),identity) = double_divide(double_divide(X3,double_divide(double_divide(X,double_divide(X2,X3)),inverse(X2))),inverse(identity)),
inference(congruence,[status(thm)],[c314]) ).
cnf(c316,plain,
double_divide(double_divide(X3,double_divide(double_divide(X,double_divide(X2,X3)),inverse(X2))),inverse(identity)) = X,
inference(substitution,[status(thm)],[c19]) ).
cnf(c317,plain,
double_divide(double_divide(X3,double_divide(double_divide(X,double_divide(X2,X3)),inverse(X2))),identity) = X,
inference(transitivity,[status(thm)],[c315,c316]) ).
cnf(c318,plain,
inverse(double_divide(X3,double_divide(double_divide(X,double_divide(X2,X3)),inverse(X2)))) = X,
inference(transitivity,[status(thm)],[c313,c317]) ).
cnf(c319,plain,
multiply(X3,double_divide(double_divide(X,double_divide(X2,X3)),inverse(X2))) = X,
inference(transitivity,[status(thm)],[c312,c318]) ).
cnf(c320,plain,
multiply(X3,multiply(X2,inverse(double_divide(X,double_divide(X2,X3))))) = X,
inference(transitivity,[status(thm)],[c310,c319]) ).
cnf(c321,plain,
multiply(X3,multiply(X2,multiply(X,double_divide(X2,X3)))) = X,
inference(transitivity,[status(thm)],[c267,c320]) ).
cnf(c322,plain,
multiply(X3,multiply(X2,multiply(X,multiply(inverse(X2),inverse(X3))))) = X,
inference(transitivity,[status(thm)],[c263,c321]) ).
cnf(c323,plain,
multiply(X3,multiply(X2,multiply(X,multiply(inverse(X3),inverse(X2))))) = X,
inference(transitivity,[status(thm)],[c210,c322]) ).
cnf(c324,plain,
multiply(X2,multiply(X,multiply(double_divide(inverse(X3),multiply(inverse(X2),inverse(X))),multiply(inverse(X2),inverse(X))))) = double_divide(inverse(X3),multiply(inverse(X2),inverse(X))),
inference(substitution,[status(thm)],[c323]) ).
cnf(c325,plain,
double_divide(inverse(X2),X) = double_divide(X,inverse(X2)),
inference(substitution,[status(thm)],[c243]) ).
cnf(c326,plain,
double_divide(X,inverse(X2)) = multiply(X2,inverse(X)),
inference(substitution,[status(thm)],[c307]) ).
cnf(c327,plain,
double_divide(inverse(X2),X) = multiply(X2,inverse(X)),
inference(transitivity,[status(thm)],[c325,c326]) ).
cnf(c328,plain,
double_divide(inverse(X3),multiply(inverse(X2),inverse(X))) = multiply(X3,inverse(multiply(inverse(X2),inverse(X)))),
inference(substitution,[status(thm)],[c327]) ).
cnf(c329,plain,
inverse(multiply(inverse(X2),inverse(X))) = double_divide(inverse(X2),inverse(X)),
inference(substitution,[status(thm)],[c236]) ).
cnf(c330,plain,
multiply(X3,inverse(multiply(inverse(X2),inverse(X)))) = multiply(X3,double_divide(inverse(X2),inverse(X))),
inference(congruence,[status(thm)],[c329]) ).
cnf(c331,plain,
double_divide(inverse(X2),inverse(X)) = multiply(X2,inverse(inverse(X))),
inference(substitution,[status(thm)],[c327]) ).
cnf(c332,plain,
multiply(X3,double_divide(inverse(X2),inverse(X))) = multiply(X3,multiply(X2,inverse(inverse(X)))),
inference(congruence,[status(thm)],[c331]) ).
cnf(c333,plain,
multiply(X2,inverse(inverse(X))) = multiply(X2,X),
inference(congruence,[status(thm)],[c155]) ).
cnf(c334,plain,
multiply(X3,multiply(X2,inverse(inverse(X)))) = multiply(X3,multiply(X2,X)),
inference(congruence,[status(thm)],[c333]) ).
cnf(c335,plain,
multiply(X3,double_divide(inverse(X2),inverse(X))) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c332,c334]) ).
cnf(c336,plain,
multiply(X3,inverse(multiply(inverse(X2),inverse(X)))) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c330,c335]) ).
cnf(c337,plain,
double_divide(inverse(X3),multiply(inverse(X2),inverse(X))) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c328,c336]) ).
cnf(c338,plain,
multiply(X2,multiply(X,multiply(double_divide(inverse(X3),multiply(inverse(X2),inverse(X))),multiply(inverse(X2),inverse(X))))) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c324,c337]) ).
cnf(c339,plain,
multiply(X2,multiply(X,X3)) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c205,c338]) ).
cnf(c340,plain,
multiply(X2,multiply(X3,X)) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c183,c339]) ).
cnf(c341,plain,
multiply(a3,multiply(c3,b3)) = multiply(c3,multiply(a3,b3)),
inference(substitution,[status(thm)],[c340]) ).
cnf(c342,plain,
multiply(c3,multiply(a3,b3)) = multiply(a3,multiply(c3,b3)),
inference(symmetry,[status(thm)],[c341]) ).
cnf(c343,plain,
multiply(c3,b3) = multiply(b3,c3),
inference(substitution,[status(thm)],[c179]) ).
cnf(c344,plain,
multiply(a3,multiply(c3,b3)) = multiply(a3,multiply(b3,c3)),
inference(congruence,[status(thm)],[c343]) ).
cnf(c345,plain,
multiply(c3,multiply(a3,b3)) = multiply(a3,multiply(b3,c3)),
inference(transitivity,[status(thm)],[c342,c344]) ).
cnf(c346,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(transitivity,[status(thm)],[c180,c345]) ).
cnf(c347,plain,
$false,
inference(resolution,[status(thm)],[c1,c346]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP575-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.39 % Computer : n007.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 10:05:09 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.32/0.55 Command-line arguments: --no-flatten-goal
% 0.32/0.55
% 0.32/0.55 % SZS status Unsatisfiable
% 0.32/0.55
% 0.32/0.58 % SZS output start CNFRefutation
% See solution above
% 2.43/0.82
% 2.43/0.82 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------