%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP489-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 10:10:48 AM UTC 2026
% Result : Unsatisfiable 0.55s 0.52s
% Output : CNFRefutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 163
% Number of leaves : 5
% Syntax : Number of clauses : 626 ( 626 unt; 0 nHn; 27 RR)
% Number of literals : 626 ( 625 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 1129 ( 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(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
double_divide(identity,inverse(X)) = double_divide(identity,double_divide(X,identity)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
identity = double_divide(A2,inverse(A2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
cnf(c6,plain,
identity = double_divide(identity,inverse(identity)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(inverse(X),identity) = multiply(inverse(X),double_divide(identity,inverse(identity))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
double_divide(X,multiply(inverse(X),identity)) = double_divide(X,multiply(inverse(X),double_divide(identity,inverse(identity)))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
inverse(double_divide(X,X2)) = double_divide(double_divide(X,X2),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,axiom,
multiply(A2,B) = double_divide(double_divide(B,A2),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(c11,plain,
multiply(X,X2) = double_divide(double_divide(X2,X),identity),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
double_divide(double_divide(X2,X),identity) = multiply(X,X2),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
inverse(double_divide(X2,X)) = multiply(X,X2),
inference(transitivity,[status(thm)],[c9,c12]) ).
cnf(c14,plain,
inverse(double_divide(identity,inverse(inverse(X)))) = multiply(inverse(inverse(X)),identity),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(inverse(inverse(X)),identity) = inverse(double_divide(identity,inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
inverse(multiply(inverse(inverse(X)),identity)) = inverse(inverse(double_divide(identity,inverse(inverse(X))))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
inverse(inverse(X)) = double_divide(inverse(X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c18,plain,
double_divide(identity,inverse(inverse(X))) = double_divide(identity,double_divide(inverse(X),identity)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(X,double_divide(identity,inverse(inverse(X2)))) = multiply(X,double_divide(identity,double_divide(inverse(X2),identity))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
double_divide(X2,multiply(X,double_divide(identity,inverse(inverse(X2))))) = double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),identity)))),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
identity = double_divide(X,inverse(X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c22,plain,
double_divide(inverse(X2),identity) = double_divide(inverse(X2),double_divide(X,inverse(X))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
double_divide(identity,double_divide(inverse(X2),identity)) = double_divide(identity,double_divide(inverse(X2),double_divide(X,inverse(X)))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(X,double_divide(identity,double_divide(inverse(X2),identity))) = multiply(X,double_divide(identity,double_divide(inverse(X2),double_divide(X,inverse(X))))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),identity)))) = double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),double_divide(X,inverse(X)))))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c27,plain,
double_divide(inverse(X2),double_divide(X,X3)) = double_divide(double_divide(X2,identity),double_divide(X,X3)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
double_divide(identity,double_divide(inverse(X3),double_divide(X2,X))) = double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
multiply(X2,double_divide(identity,double_divide(inverse(X3),double_divide(X2,X)))) = multiply(X2,double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X)))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
double_divide(X3,multiply(X2,double_divide(identity,double_divide(inverse(X3),double_divide(X2,X))))) = double_divide(X3,multiply(X2,double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
inverse(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),X2)) = multiply(X2,double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X)))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c32,plain,
multiply(X2,double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X)))) = inverse(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),X2)),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
double_divide(X3,multiply(X2,double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))))) = double_divide(X3,inverse(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),X2))),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
inverse(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),X2)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),X2),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c35,plain,
double_divide(X3,inverse(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),X2))) = double_divide(X3,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),X2),identity)),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,axiom,
double_divide(A2,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A2,identity),double_divide(B2,C))),B2),identity)) = C,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(c37,plain,
double_divide(X3,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),X2),identity)) = X,
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
double_divide(X3,inverse(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))),X2))) = X,
inference(transitivity,[status(thm)],[c35,c37]) ).
cnf(c39,plain,
double_divide(X3,multiply(X2,double_divide(identity,double_divide(double_divide(X3,identity),double_divide(X2,X))))) = X,
inference(transitivity,[status(thm)],[c33,c38]) ).
cnf(c40,plain,
double_divide(X3,multiply(X2,double_divide(identity,double_divide(inverse(X3),double_divide(X2,X))))) = X,
inference(transitivity,[status(thm)],[c30,c39]) ).
cnf(c41,plain,
double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),double_divide(X,inverse(X)))))) = inverse(X),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),identity)))) = inverse(X),
inference(transitivity,[status(thm)],[c25,c41]) ).
cnf(c43,plain,
double_divide(X2,multiply(X,double_divide(identity,inverse(inverse(X2))))) = inverse(X),
inference(transitivity,[status(thm)],[c20,c42]) ).
cnf(c44,plain,
double_divide(X,multiply(inverse(double_divide(identity,inverse(inverse(X)))),double_divide(identity,inverse(inverse(X))))) = inverse(inverse(double_divide(identity,inverse(inverse(X))))),
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
inverse(inverse(double_divide(identity,inverse(inverse(X))))) = double_divide(X,multiply(inverse(double_divide(identity,inverse(inverse(X)))),double_divide(identity,inverse(inverse(X))))),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
inverse(double_divide(X,inverse(X))) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c47,plain,
multiply(inverse(X),X) = inverse(double_divide(X,inverse(X))),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
identity = double_divide(X,inverse(X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c49,plain,
double_divide(X,inverse(X)) = identity,
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
inverse(double_divide(X,inverse(X))) = inverse(identity),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(inverse(X),X) = inverse(identity),
inference(transitivity,[status(thm)],[c47,c50]) ).
cnf(c52,plain,
multiply(inverse(double_divide(identity,inverse(inverse(X)))),double_divide(identity,inverse(inverse(X)))) = inverse(identity),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
double_divide(X,multiply(inverse(double_divide(identity,inverse(inverse(X)))),double_divide(identity,inverse(inverse(X))))) = double_divide(X,inverse(identity)),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
inverse(inverse(double_divide(identity,inverse(inverse(X))))) = double_divide(X,inverse(identity)),
inference(transitivity,[status(thm)],[c45,c53]) ).
cnf(c55,plain,
inverse(multiply(inverse(inverse(X)),identity)) = double_divide(X,inverse(identity)),
inference(transitivity,[status(thm)],[c16,c54]) ).
cnf(c56,plain,
double_divide(X,inverse(identity)) = inverse(multiply(inverse(inverse(X)),identity)),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
double_divide(X,double_divide(X,inverse(identity))) = double_divide(X,inverse(multiply(inverse(inverse(X)),identity))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
inverse(double_divide(identity,inverse(inverse(X)))) = multiply(inverse(inverse(X)),identity),
inference(substitution,[status(thm)],[c13]) ).
cnf(c59,plain,
multiply(inverse(inverse(X)),identity) = inverse(double_divide(identity,inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
inverse(multiply(inverse(inverse(X)),identity)) = inverse(inverse(double_divide(identity,inverse(inverse(X))))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
double_divide(X,inverse(multiply(inverse(inverse(X)),identity))) = double_divide(X,inverse(inverse(double_divide(identity,inverse(inverse(X)))))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
inverse(double_divide(X,identity)) = multiply(identity,X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c63,plain,
multiply(identity,X) = inverse(double_divide(X,identity)),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c65,plain,
double_divide(X,identity) = inverse(X),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
inverse(double_divide(X,identity)) = inverse(inverse(X)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
multiply(identity,X) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c63,c66]) ).
cnf(c68,plain,
multiply(identity,double_divide(identity,inverse(inverse(X)))) = inverse(inverse(double_divide(identity,inverse(inverse(X))))),
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
inverse(inverse(double_divide(identity,inverse(inverse(X))))) = multiply(identity,double_divide(identity,inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
double_divide(X,inverse(inverse(double_divide(identity,inverse(inverse(X)))))) = double_divide(X,multiply(identity,double_divide(identity,inverse(inverse(X))))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
double_divide(X,multiply(identity,double_divide(identity,inverse(inverse(X))))) = inverse(identity),
inference(substitution,[status(thm)],[c43]) ).
cnf(c72,plain,
double_divide(X,inverse(inverse(double_divide(identity,inverse(inverse(X)))))) = inverse(identity),
inference(transitivity,[status(thm)],[c70,c71]) ).
cnf(c73,plain,
double_divide(X,inverse(multiply(inverse(inverse(X)),identity))) = inverse(identity),
inference(transitivity,[status(thm)],[c61,c72]) ).
cnf(c74,plain,
double_divide(X,double_divide(X,inverse(identity))) = inverse(identity),
inference(transitivity,[status(thm)],[c57,c73]) ).
cnf(c75,plain,
double_divide(inverse(X),double_divide(inverse(X),inverse(identity))) = inverse(identity),
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
inverse(identity) = double_divide(inverse(X),double_divide(inverse(X),inverse(identity))),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
double_divide(identity,inverse(identity)) = double_divide(identity,double_divide(inverse(X),double_divide(inverse(X),inverse(identity)))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
multiply(inverse(X),double_divide(identity,inverse(identity))) = multiply(inverse(X),double_divide(identity,double_divide(inverse(X),double_divide(inverse(X),inverse(identity))))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
double_divide(X,multiply(inverse(X),double_divide(identity,inverse(identity)))) = double_divide(X,multiply(inverse(X),double_divide(identity,double_divide(inverse(X),double_divide(inverse(X),inverse(identity)))))),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
double_divide(X,multiply(inverse(X),double_divide(identity,double_divide(inverse(X),double_divide(inverse(X),inverse(identity)))))) = inverse(identity),
inference(substitution,[status(thm)],[c40]) ).
cnf(c81,plain,
double_divide(X,multiply(inverse(X),double_divide(identity,inverse(identity)))) = inverse(identity),
inference(transitivity,[status(thm)],[c79,c80]) ).
cnf(c82,plain,
double_divide(X,multiply(inverse(X),identity)) = inverse(identity),
inference(transitivity,[status(thm)],[c8,c81]) ).
cnf(c83,plain,
double_divide(identity,multiply(inverse(identity),identity)) = inverse(identity),
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
inverse(identity) = double_divide(identity,multiply(inverse(identity),identity)),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
multiply(inverse(identity),identity) = inverse(identity),
inference(substitution,[status(thm)],[c51]) ).
cnf(c86,plain,
double_divide(identity,multiply(inverse(identity),identity)) = double_divide(identity,inverse(identity)),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
identity = double_divide(identity,inverse(identity)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c88,plain,
double_divide(identity,inverse(identity)) = identity,
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
double_divide(identity,multiply(inverse(identity),identity)) = identity,
inference(transitivity,[status(thm)],[c86,c88]) ).
cnf(c90,plain,
inverse(identity) = identity,
inference(transitivity,[status(thm)],[c84,c89]) ).
cnf(c91,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
double_divide(X,identity) = double_divide(X,inverse(identity)),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
double_divide(identity,double_divide(X,identity)) = double_divide(identity,double_divide(X,inverse(identity))),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
double_divide(X,inverse(identity)) = inverse(multiply(inverse(inverse(X)),identity)),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c95,plain,
double_divide(identity,double_divide(X,inverse(identity))) = double_divide(identity,inverse(multiply(inverse(inverse(X)),identity))),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
inverse(double_divide(identity,inverse(inverse(X)))) = multiply(inverse(inverse(X)),identity),
inference(substitution,[status(thm)],[c13]) ).
cnf(c97,plain,
multiply(inverse(inverse(X)),identity) = inverse(double_divide(identity,inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
inverse(multiply(inverse(inverse(X)),identity)) = inverse(inverse(double_divide(identity,inverse(inverse(X))))),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
double_divide(identity,inverse(multiply(inverse(inverse(X)),identity))) = double_divide(identity,inverse(inverse(double_divide(identity,inverse(inverse(X)))))),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
identity = double_divide(identity,inverse(identity)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c101,plain,
multiply(X,identity) = multiply(X,double_divide(identity,inverse(identity))),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
double_divide(identity,multiply(X,identity)) = double_divide(identity,multiply(X,double_divide(identity,inverse(identity)))),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c104,plain,
inverse(identity) = inverse(inverse(identity)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
double_divide(identity,inverse(identity)) = double_divide(identity,inverse(inverse(identity))),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
multiply(X,double_divide(identity,inverse(identity))) = multiply(X,double_divide(identity,inverse(inverse(identity)))),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
double_divide(identity,multiply(X,double_divide(identity,inverse(identity)))) = double_divide(identity,multiply(X,double_divide(identity,inverse(inverse(identity))))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
double_divide(identity,multiply(X,double_divide(identity,inverse(inverse(identity))))) = inverse(X),
inference(substitution,[status(thm)],[c43]) ).
cnf(c109,plain,
double_divide(identity,multiply(X,double_divide(identity,inverse(identity)))) = inverse(X),
inference(transitivity,[status(thm)],[c107,c108]) ).
cnf(c110,plain,
double_divide(identity,multiply(X,identity)) = inverse(X),
inference(transitivity,[status(thm)],[c102,c109]) ).
cnf(c111,plain,
double_divide(identity,multiply(multiply(X,identity),identity)) = inverse(multiply(X,identity)),
inference(substitution,[status(thm)],[c110]) ).
cnf(c112,plain,
inverse(multiply(X,identity)) = double_divide(identity,multiply(multiply(X,identity),identity)),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
inverse(double_divide(identity,multiply(X,identity))) = multiply(multiply(X,identity),identity),
inference(substitution,[status(thm)],[c13]) ).
cnf(c114,plain,
multiply(multiply(X,identity),identity) = inverse(double_divide(identity,multiply(X,identity))),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
inverse(double_divide(identity,multiply(X,identity))) = inverse(inverse(X)),
inference(congruence,[status(thm)],[c110]) ).
cnf(c116,plain,
multiply(multiply(X,identity),identity) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c114,c115]) ).
cnf(c117,plain,
double_divide(identity,multiply(multiply(X,identity),identity)) = double_divide(identity,inverse(inverse(X))),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
inverse(multiply(X,identity)) = double_divide(identity,inverse(inverse(X))),
inference(transitivity,[status(thm)],[c112,c117]) ).
cnf(c119,plain,
double_divide(identity,inverse(inverse(X))) = inverse(multiply(X,identity)),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
inverse(double_divide(identity,inverse(inverse(X)))) = inverse(inverse(multiply(X,identity))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
inverse(inverse(double_divide(identity,inverse(inverse(X))))) = inverse(inverse(inverse(multiply(X,identity)))),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
double_divide(identity,inverse(inverse(double_divide(identity,inverse(inverse(X)))))) = double_divide(identity,inverse(inverse(inverse(multiply(X,identity))))),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
inverse(multiply(inverse(multiply(X2,X)),identity)) = double_divide(identity,inverse(inverse(inverse(multiply(X2,X))))),
inference(substitution,[status(thm)],[c118]) ).
cnf(c124,plain,
double_divide(identity,inverse(inverse(inverse(multiply(X2,X))))) = inverse(multiply(inverse(multiply(X2,X)),identity)),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c126,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
inverse(multiply(X2,X)) = inverse(inverse(double_divide(X,X2))),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
multiply(inverse(multiply(X2,X)),identity) = multiply(inverse(inverse(double_divide(X,X2))),identity),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
inverse(multiply(inverse(multiply(X2,X)),identity)) = inverse(multiply(inverse(inverse(double_divide(X,X2))),identity)),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
inverse(multiply(inverse(inverse(double_divide(X,X2))),identity)) = double_divide(double_divide(X,X2),inverse(identity)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c131,plain,
double_divide(double_divide(X,X2),inverse(identity)) = double_divide(double_divide(X,X2),identity),
inference(congruence,[status(thm)],[c90]) ).
cnf(c132,plain,
inverse(double_divide(X,X2)) = double_divide(double_divide(X,X2),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c133,plain,
double_divide(double_divide(X,X2),identity) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c135,plain,
double_divide(double_divide(X,X2),identity) = multiply(X2,X),
inference(transitivity,[status(thm)],[c133,c134]) ).
cnf(c136,plain,
double_divide(double_divide(X,X2),inverse(identity)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c131,c135]) ).
cnf(c137,plain,
inverse(multiply(inverse(inverse(double_divide(X,X2))),identity)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c130,c136]) ).
cnf(c138,plain,
inverse(multiply(inverse(multiply(X2,X)),identity)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c129,c137]) ).
cnf(c139,plain,
double_divide(identity,inverse(inverse(inverse(multiply(X2,X))))) = multiply(X2,X),
inference(transitivity,[status(thm)],[c124,c138]) ).
cnf(c140,plain,
double_divide(identity,inverse(inverse(inverse(multiply(X,identity))))) = multiply(X,identity),
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,plain,
double_divide(identity,inverse(inverse(double_divide(identity,inverse(inverse(X)))))) = multiply(X,identity),
inference(transitivity,[status(thm)],[c122,c140]) ).
cnf(c142,plain,
double_divide(identity,inverse(multiply(inverse(inverse(X)),identity))) = multiply(X,identity),
inference(transitivity,[status(thm)],[c99,c141]) ).
cnf(c143,plain,
double_divide(identity,double_divide(X,inverse(identity))) = multiply(X,identity),
inference(transitivity,[status(thm)],[c95,c142]) ).
cnf(c144,plain,
double_divide(identity,double_divide(X,identity)) = multiply(X,identity),
inference(transitivity,[status(thm)],[c93,c143]) ).
cnf(c145,plain,
double_divide(identity,inverse(X)) = multiply(X,identity),
inference(transitivity,[status(thm)],[c4,c144]) ).
cnf(c146,plain,
double_divide(identity,inverse(multiply(X2,X))) = multiply(multiply(X2,X),identity),
inference(substitution,[status(thm)],[c145]) ).
cnf(c147,plain,
multiply(multiply(X2,X),identity) = double_divide(identity,inverse(multiply(X2,X))),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
inverse(inverse(multiply(X2,X))) = double_divide(inverse(multiply(X2,X)),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c149,plain,
inverse(double_divide(X,multiply(inverse(X),identity))) = multiply(multiply(inverse(X),identity),X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c150,plain,
multiply(multiply(inverse(X),identity),X) = inverse(double_divide(X,multiply(inverse(X),identity))),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,plain,
inverse(double_divide(X,multiply(inverse(X),identity))) = inverse(inverse(identity)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c152,plain,
inverse(inverse(identity)) = inverse(identity),
inference(congruence,[status(thm)],[c90]) ).
cnf(c153,plain,
inverse(inverse(identity)) = identity,
inference(transitivity,[status(thm)],[c152,c90]) ).
cnf(c154,plain,
inverse(double_divide(X,multiply(inverse(X),identity))) = identity,
inference(transitivity,[status(thm)],[c151,c153]) ).
cnf(c155,plain,
multiply(multiply(inverse(X),identity),X) = identity,
inference(transitivity,[status(thm)],[c150,c154]) ).
cnf(c156,plain,
multiply(multiply(inverse(multiply(X2,X)),identity),multiply(X2,X)) = identity,
inference(substitution,[status(thm)],[c155]) ).
cnf(c157,plain,
identity = multiply(multiply(inverse(multiply(X2,X)),identity),multiply(X2,X)),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
double_divide(inverse(multiply(X2,X)),identity) = double_divide(inverse(multiply(X2,X)),multiply(multiply(inverse(multiply(X2,X)),identity),multiply(X2,X))),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
multiply(X2,X) = double_divide(identity,inverse(inverse(inverse(multiply(X2,X))))),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c160,plain,
multiply(X,multiply(X3,X2)) = multiply(X,double_divide(identity,inverse(inverse(inverse(multiply(X3,X2)))))),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
double_divide(inverse(multiply(X3,X2)),multiply(X,multiply(X3,X2))) = double_divide(inverse(multiply(X3,X2)),multiply(X,double_divide(identity,inverse(inverse(inverse(multiply(X3,X2))))))),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
double_divide(inverse(multiply(X3,X2)),multiply(X,double_divide(identity,inverse(inverse(inverse(multiply(X3,X2))))))) = inverse(X),
inference(substitution,[status(thm)],[c43]) ).
cnf(c163,plain,
double_divide(inverse(multiply(X3,X2)),multiply(X,multiply(X3,X2))) = inverse(X),
inference(transitivity,[status(thm)],[c161,c162]) ).
cnf(c164,plain,
double_divide(inverse(multiply(X2,X)),multiply(multiply(inverse(multiply(X2,X)),identity),multiply(X2,X))) = inverse(multiply(inverse(multiply(X2,X)),identity)),
inference(substitution,[status(thm)],[c163]) ).
cnf(c165,plain,
inverse(multiply(inverse(multiply(X2,X)),identity)) = double_divide(identity,inverse(inverse(inverse(multiply(X2,X))))),
inference(substitution,[status(thm)],[c118]) ).
cnf(c166,plain,
inverse(multiply(inverse(multiply(X2,X)),identity)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c165,c139]) ).
cnf(c167,plain,
double_divide(inverse(multiply(X2,X)),multiply(multiply(inverse(multiply(X2,X)),identity),multiply(X2,X))) = multiply(X2,X),
inference(transitivity,[status(thm)],[c164,c166]) ).
cnf(c168,plain,
double_divide(inverse(multiply(X2,X)),identity) = multiply(X2,X),
inference(transitivity,[status(thm)],[c158,c167]) ).
cnf(c169,plain,
inverse(inverse(multiply(X2,X))) = multiply(X2,X),
inference(transitivity,[status(thm)],[c148,c168]) ).
cnf(c170,plain,
multiply(X2,X) = inverse(inverse(multiply(X2,X))),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
inverse(multiply(X2,X)) = inverse(inverse(inverse(multiply(X2,X)))),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
double_divide(identity,inverse(multiply(X2,X))) = double_divide(identity,inverse(inverse(inverse(multiply(X2,X))))),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
double_divide(identity,inverse(multiply(X2,X))) = multiply(X2,X),
inference(transitivity,[status(thm)],[c172,c139]) ).
cnf(c174,plain,
multiply(multiply(X2,X),identity) = multiply(X2,X),
inference(transitivity,[status(thm)],[c147,c173]) ).
cnf(c175,plain,
multiply(multiply(X,identity),identity) = multiply(X,identity),
inference(substitution,[status(thm)],[c174]) ).
cnf(c176,plain,
multiply(X,identity) = multiply(multiply(X,identity),identity),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
multiply(X,identity) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c176,c116]) ).
cnf(c178,plain,
inverse(inverse(X)) = multiply(X,identity),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c179,plain,
inverse(double_divide(identity,X)) = multiply(X,identity),
inference(substitution,[status(thm)],[c13]) ).
cnf(c180,plain,
multiply(X,identity) = inverse(double_divide(identity,X)),
inference(symmetry,[status(thm)],[c179]) ).
cnf(c181,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c182,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
inverse(multiply(X2,X)) = inverse(inverse(double_divide(X,X2))),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
multiply(inverse(X3),inverse(multiply(X2,X))) = multiply(inverse(X3),inverse(inverse(double_divide(X,X2)))),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
multiply(inverse(X),identity) = inverse(inverse(inverse(X))),
inference(substitution,[status(thm)],[c177]) ).
cnf(c186,plain,
inverse(inverse(inverse(X))) = multiply(inverse(X),identity),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,plain,
double_divide(identity,inverse(inverse(X))) = multiply(inverse(X),identity),
inference(substitution,[status(thm)],[c145]) ).
cnf(c188,plain,
multiply(inverse(X),identity) = double_divide(identity,inverse(inverse(X))),
inference(symmetry,[status(thm)],[c187]) ).
cnf(c189,plain,
inverse(inverse(X)) = multiply(X,identity),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c190,plain,
double_divide(identity,inverse(inverse(X))) = double_divide(identity,multiply(X,identity)),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
double_divide(identity,inverse(inverse(X))) = inverse(X),
inference(transitivity,[status(thm)],[c190,c110]) ).
cnf(c192,plain,
multiply(inverse(X),identity) = inverse(X),
inference(transitivity,[status(thm)],[c188,c191]) ).
cnf(c193,plain,
inverse(inverse(inverse(X))) = inverse(X),
inference(transitivity,[status(thm)],[c186,c192]) ).
cnf(c194,plain,
inverse(inverse(inverse(inverse(X)))) = inverse(inverse(X)),
inference(substitution,[status(thm)],[c193]) ).
cnf(c195,plain,
inverse(inverse(X)) = inverse(inverse(inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c194]) ).
cnf(c196,plain,
multiply(inverse(X2),inverse(inverse(X))) = multiply(inverse(X2),inverse(inverse(inverse(inverse(X))))),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
inverse(X) = inverse(inverse(inverse(X))),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c198,plain,
multiply(X2,inverse(X)) = multiply(X2,inverse(inverse(inverse(X)))),
inference(congruence,[status(thm)],[c197]) ).
cnf(c199,plain,
multiply(multiply(X2,inverse(X)),X) = multiply(multiply(X2,inverse(inverse(inverse(X)))),X),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
multiply(inverse(X),identity) = inverse(inverse(inverse(X))),
inference(substitution,[status(thm)],[c177]) ).
cnf(c201,plain,
inverse(inverse(inverse(X))) = multiply(inverse(X),identity),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c202,plain,
multiply(X2,inverse(inverse(inverse(X)))) = multiply(X2,multiply(inverse(X),identity)),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
multiply(multiply(X2,inverse(inverse(inverse(X)))),X) = multiply(multiply(X2,multiply(inverse(X),identity)),X),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
double_divide(identity,inverse(inverse(X))) = multiply(inverse(X),identity),
inference(substitution,[status(thm)],[c145]) ).
cnf(c205,plain,
multiply(inverse(X),identity) = double_divide(identity,inverse(inverse(X))),
inference(symmetry,[status(thm)],[c204]) ).
cnf(c206,plain,
multiply(X2,multiply(inverse(X),identity)) = multiply(X2,double_divide(identity,inverse(inverse(X)))),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
multiply(multiply(X2,multiply(inverse(X),identity)),X) = multiply(multiply(X2,double_divide(identity,inverse(inverse(X)))),X),
inference(congruence,[status(thm)],[c206]) ).
cnf(c208,plain,
inverse(double_divide(X,multiply(X2,double_divide(identity,inverse(inverse(X)))))) = multiply(multiply(X2,double_divide(identity,inverse(inverse(X)))),X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c209,plain,
multiply(multiply(X2,double_divide(identity,inverse(inverse(X)))),X) = inverse(double_divide(X,multiply(X2,double_divide(identity,inverse(inverse(X)))))),
inference(symmetry,[status(thm)],[c208]) ).
cnf(c210,plain,
double_divide(X,multiply(X2,double_divide(identity,inverse(inverse(X))))) = inverse(X2),
inference(substitution,[status(thm)],[c43]) ).
cnf(c211,plain,
inverse(double_divide(X,multiply(X2,double_divide(identity,inverse(inverse(X)))))) = inverse(inverse(X2)),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
multiply(multiply(X2,double_divide(identity,inverse(inverse(X)))),X) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c209,c211]) ).
cnf(c213,plain,
multiply(multiply(X2,multiply(inverse(X),identity)),X) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c207,c212]) ).
cnf(c214,plain,
multiply(multiply(X2,inverse(inverse(inverse(X)))),X) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c203,c213]) ).
cnf(c215,plain,
multiply(multiply(X2,inverse(X)),X) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c199,c214]) ).
cnf(c216,plain,
multiply(multiply(X2,inverse(inverse(X))),inverse(X)) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c215]) ).
cnf(c217,plain,
inverse(inverse(X2)) = multiply(multiply(X2,inverse(inverse(X))),inverse(X)),
inference(symmetry,[status(thm)],[c216]) ).
cnf(c218,plain,
multiply(inverse(inverse(X2)),X) = multiply(multiply(multiply(X2,inverse(inverse(X))),inverse(X)),X),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
multiply(multiply(multiply(X2,inverse(inverse(X))),inverse(X)),X) = inverse(inverse(multiply(X2,inverse(inverse(X))))),
inference(substitution,[status(thm)],[c215]) ).
cnf(c220,plain,
inverse(inverse(multiply(X2,inverse(inverse(X))))) = multiply(X2,inverse(inverse(X))),
inference(substitution,[status(thm)],[c169]) ).
cnf(c221,plain,
multiply(multiply(multiply(X2,inverse(inverse(X))),inverse(X)),X) = multiply(X2,inverse(inverse(X))),
inference(transitivity,[status(thm)],[c219,c220]) ).
cnf(c222,plain,
multiply(inverse(inverse(X2)),X) = multiply(X2,inverse(inverse(X))),
inference(transitivity,[status(thm)],[c218,c221]) ).
cnf(c223,plain,
multiply(inverse(inverse(inverse(X2))),inverse(inverse(X))) = multiply(inverse(X2),inverse(inverse(inverse(inverse(X))))),
inference(substitution,[status(thm)],[c222]) ).
cnf(c224,plain,
multiply(inverse(X2),inverse(inverse(inverse(inverse(X))))) = multiply(inverse(inverse(inverse(X2))),inverse(inverse(X))),
inference(symmetry,[status(thm)],[c223]) ).
cnf(c225,plain,
multiply(inverse(X),identity) = inverse(inverse(inverse(X))),
inference(substitution,[status(thm)],[c177]) ).
cnf(c226,plain,
inverse(inverse(inverse(X))) = multiply(inverse(X),identity),
inference(symmetry,[status(thm)],[c225]) ).
cnf(c227,plain,
multiply(inverse(inverse(inverse(X2))),inverse(inverse(X))) = multiply(multiply(inverse(X2),identity),inverse(inverse(X))),
inference(congruence,[status(thm)],[c226]) ).
cnf(c228,plain,
double_divide(identity,inverse(inverse(X))) = multiply(inverse(X),identity),
inference(substitution,[status(thm)],[c145]) ).
cnf(c229,plain,
multiply(inverse(X),identity) = double_divide(identity,inverse(inverse(X))),
inference(symmetry,[status(thm)],[c228]) ).
cnf(c230,plain,
multiply(multiply(inverse(X2),identity),inverse(inverse(X))) = multiply(double_divide(identity,inverse(inverse(X2))),inverse(inverse(X))),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c232,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c233,plain,
inverse(multiply(X2,X)) = inverse(inverse(double_divide(X,X2))),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
multiply(inverse(multiply(X3,X2)),X) = multiply(inverse(inverse(double_divide(X2,X3))),X),
inference(congruence,[status(thm)],[c233]) ).
cnf(c235,plain,
multiply(inverse(inverse(double_divide(X2,X3))),X) = multiply(double_divide(X2,X3),inverse(inverse(X))),
inference(substitution,[status(thm)],[c222]) ).
cnf(c236,plain,
multiply(inverse(multiply(X3,X2)),X) = multiply(double_divide(X2,X3),inverse(inverse(X))),
inference(transitivity,[status(thm)],[c234,c235]) ).
cnf(c237,plain,
multiply(inverse(multiply(inverse(inverse(X2)),identity)),X) = multiply(double_divide(identity,inverse(inverse(X2))),inverse(inverse(X))),
inference(substitution,[status(thm)],[c236]) ).
cnf(c238,plain,
multiply(double_divide(identity,inverse(inverse(X2))),inverse(inverse(X))) = multiply(inverse(multiply(inverse(inverse(X2)),identity)),X),
inference(symmetry,[status(thm)],[c237]) ).
cnf(c239,plain,
multiply(inverse(multiply(inverse(inverse(X2)),identity)),X) = multiply(double_divide(X2,inverse(identity)),X),
inference(congruence,[status(thm)],[c55]) ).
cnf(c240,plain,
double_divide(X,inverse(identity)) = double_divide(X,identity),
inference(congruence,[status(thm)],[c90]) ).
cnf(c241,plain,
multiply(double_divide(X2,inverse(identity)),X) = multiply(double_divide(X2,identity),X),
inference(congruence,[status(thm)],[c240]) ).
cnf(c242,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c243,plain,
double_divide(X,identity) = inverse(X),
inference(symmetry,[status(thm)],[c242]) ).
cnf(c244,plain,
multiply(double_divide(X2,identity),X) = multiply(inverse(X2),X),
inference(congruence,[status(thm)],[c243]) ).
cnf(c245,plain,
multiply(double_divide(X2,inverse(identity)),X) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c241,c244]) ).
cnf(c246,plain,
multiply(inverse(multiply(inverse(inverse(X2)),identity)),X) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c239,c245]) ).
cnf(c247,plain,
multiply(double_divide(identity,inverse(inverse(X2))),inverse(inverse(X))) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c238,c246]) ).
cnf(c248,plain,
multiply(multiply(inverse(X2),identity),inverse(inverse(X))) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c230,c247]) ).
cnf(c249,plain,
multiply(inverse(inverse(inverse(X2))),inverse(inverse(X))) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c227,c248]) ).
cnf(c250,plain,
multiply(inverse(X2),inverse(inverse(inverse(inverse(X))))) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c224,c249]) ).
cnf(c251,plain,
multiply(inverse(X2),inverse(inverse(X))) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c196,c250]) ).
cnf(c252,plain,
multiply(inverse(X3),inverse(inverse(double_divide(X,X2)))) = multiply(inverse(X3),double_divide(X,X2)),
inference(substitution,[status(thm)],[c251]) ).
cnf(c253,plain,
multiply(inverse(X3),inverse(multiply(X2,X))) = multiply(inverse(X3),double_divide(X,X2)),
inference(transitivity,[status(thm)],[c184,c252]) ).
cnf(c254,plain,
multiply(inverse(X2),inverse(multiply(X,inverse(X2)))) = multiply(inverse(X2),double_divide(inverse(X2),X)),
inference(substitution,[status(thm)],[c253]) ).
cnf(c255,plain,
multiply(inverse(X2),double_divide(inverse(X2),X)) = multiply(inverse(X2),inverse(multiply(X,inverse(X2)))),
inference(symmetry,[status(thm)],[c254]) ).
cnf(c256,plain,
inverse(X) = inverse(inverse(inverse(X))),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c257,plain,
multiply(X2,inverse(X)) = multiply(X2,inverse(inverse(inverse(X)))),
inference(congruence,[status(thm)],[c256]) ).
cnf(c258,plain,
multiply(inverse(X2),multiply(X2,inverse(X))) = multiply(inverse(X2),multiply(X2,inverse(inverse(inverse(X))))),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
multiply(inverse(inverse(X2)),inverse(X)) = multiply(X2,inverse(inverse(inverse(X)))),
inference(substitution,[status(thm)],[c222]) ).
cnf(c260,plain,
multiply(X2,inverse(inverse(inverse(X)))) = multiply(inverse(inverse(X2)),inverse(X)),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c261,plain,
multiply(inverse(X2),multiply(X2,inverse(inverse(inverse(X))))) = multiply(inverse(X2),multiply(inverse(inverse(X2)),inverse(X))),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
double_divide(X,multiply(X2,double_divide(identity,double_divide(inverse(X),double_divide(X2,multiply(X3,multiply(inverse(X3),inverse(X2)))))))) = multiply(X3,multiply(inverse(X3),inverse(X2))),
inference(substitution,[status(thm)],[c40]) ).
cnf(c263,plain,
multiply(X3,multiply(inverse(X3),inverse(X2))) = double_divide(X,multiply(X2,double_divide(identity,double_divide(inverse(X),double_divide(X2,multiply(X3,multiply(inverse(X3),inverse(X2)))))))),
inference(symmetry,[status(thm)],[c262]) ).
cnf(c264,plain,
multiply(inverse(X2),X) = multiply(inverse(X2),inverse(inverse(X))),
inference(symmetry,[status(thm)],[c251]) ).
cnf(c265,plain,
inverse(multiply(inverse(X2),X)) = inverse(multiply(inverse(X2),inverse(inverse(X)))),
inference(congruence,[status(thm)],[c264]) ).
cnf(c266,plain,
inverse(inverse(X)) = multiply(X,identity),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c267,plain,
multiply(X2,inverse(inverse(X))) = multiply(X2,multiply(X,identity)),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
inverse(multiply(X2,inverse(inverse(X)))) = inverse(multiply(X2,multiply(X,identity))),
inference(congruence,[status(thm)],[c267]) ).
cnf(c269,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c270,plain,
multiply(X,identity) = multiply(X,inverse(identity)),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
multiply(X2,multiply(X,identity)) = multiply(X2,multiply(X,inverse(identity))),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
inverse(multiply(X2,multiply(X,identity))) = inverse(multiply(X2,multiply(X,inverse(identity)))),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c274,plain,
inverse(identity) = inverse(inverse(identity)),
inference(congruence,[status(thm)],[c273]) ).
cnf(c275,plain,
multiply(X,inverse(identity)) = multiply(X,inverse(inverse(identity))),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
multiply(X2,multiply(X,inverse(identity))) = multiply(X2,multiply(X,inverse(inverse(identity)))),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
inverse(multiply(X2,multiply(X,inverse(identity)))) = inverse(multiply(X2,multiply(X,inverse(inverse(identity))))),
inference(congruence,[status(thm)],[c276]) ).
cnf(c278,plain,
multiply(inverse(inverse(X)),identity) = multiply(X,inverse(inverse(identity))),
inference(substitution,[status(thm)],[c222]) ).
cnf(c279,plain,
multiply(X,inverse(inverse(identity))) = multiply(inverse(inverse(X)),identity),
inference(symmetry,[status(thm)],[c278]) ).
cnf(c280,plain,
multiply(X2,multiply(X,inverse(inverse(identity)))) = multiply(X2,multiply(inverse(inverse(X)),identity)),
inference(congruence,[status(thm)],[c279]) ).
cnf(c281,plain,
inverse(multiply(X2,multiply(X,inverse(inverse(identity))))) = inverse(multiply(X2,multiply(inverse(inverse(X)),identity))),
inference(congruence,[status(thm)],[c280]) ).
cnf(c282,plain,
inverse(double_divide(identity,inverse(inverse(X)))) = multiply(inverse(inverse(X)),identity),
inference(substitution,[status(thm)],[c13]) ).
cnf(c283,plain,
multiply(inverse(inverse(X)),identity) = inverse(double_divide(identity,inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c282]) ).
cnf(c284,plain,
multiply(X2,multiply(inverse(inverse(X)),identity)) = multiply(X2,inverse(double_divide(identity,inverse(inverse(X))))),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
inverse(multiply(X2,multiply(inverse(inverse(X)),identity))) = inverse(multiply(X2,inverse(double_divide(identity,inverse(inverse(X)))))),
inference(congruence,[status(thm)],[c284]) ).
cnf(c286,plain,
double_divide(X,multiply(multiply(X2,inverse(double_divide(identity,inverse(inverse(X))))),double_divide(identity,inverse(inverse(X))))) = inverse(multiply(X2,inverse(double_divide(identity,inverse(inverse(X)))))),
inference(substitution,[status(thm)],[c43]) ).
cnf(c287,plain,
inverse(multiply(X2,inverse(double_divide(identity,inverse(inverse(X)))))) = double_divide(X,multiply(multiply(X2,inverse(double_divide(identity,inverse(inverse(X))))),double_divide(identity,inverse(inverse(X))))),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
multiply(multiply(X2,inverse(double_divide(identity,inverse(inverse(X))))),double_divide(identity,inverse(inverse(X)))) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c215]) ).
cnf(c289,plain,
double_divide(X,multiply(multiply(X2,inverse(double_divide(identity,inverse(inverse(X))))),double_divide(identity,inverse(inverse(X))))) = double_divide(X,inverse(inverse(X2))),
inference(congruence,[status(thm)],[c288]) ).
cnf(c290,plain,
inverse(multiply(X2,inverse(double_divide(identity,inverse(inverse(X)))))) = double_divide(X,inverse(inverse(X2))),
inference(transitivity,[status(thm)],[c287,c289]) ).
cnf(c291,plain,
inverse(multiply(X2,multiply(inverse(inverse(X)),identity))) = double_divide(X,inverse(inverse(X2))),
inference(transitivity,[status(thm)],[c285,c290]) ).
cnf(c292,plain,
inverse(multiply(X2,multiply(X,inverse(inverse(identity))))) = double_divide(X,inverse(inverse(X2))),
inference(transitivity,[status(thm)],[c281,c291]) ).
cnf(c293,plain,
inverse(multiply(X2,multiply(X,inverse(identity)))) = double_divide(X,inverse(inverse(X2))),
inference(transitivity,[status(thm)],[c277,c292]) ).
cnf(c294,plain,
inverse(multiply(X2,multiply(X,identity))) = double_divide(X,inverse(inverse(X2))),
inference(transitivity,[status(thm)],[c272,c293]) ).
cnf(c295,plain,
inverse(multiply(X2,inverse(inverse(X)))) = double_divide(X,inverse(inverse(X2))),
inference(transitivity,[status(thm)],[c268,c294]) ).
cnf(c296,plain,
inverse(multiply(inverse(X2),inverse(inverse(X)))) = double_divide(X,inverse(inverse(inverse(X2)))),
inference(substitution,[status(thm)],[c295]) ).
cnf(c297,plain,
double_divide(X,inverse(inverse(inverse(X2)))) = double_divide(X,inverse(X2)),
inference(congruence,[status(thm)],[c193]) ).
cnf(c298,plain,
inverse(multiply(inverse(X2),inverse(inverse(X)))) = double_divide(X,inverse(X2)),
inference(transitivity,[status(thm)],[c296,c297]) ).
cnf(c299,plain,
inverse(multiply(inverse(X2),X)) = double_divide(X,inverse(X2)),
inference(transitivity,[status(thm)],[c265,c298]) ).
cnf(c300,plain,
inverse(multiply(inverse(X),X2)) = double_divide(X2,inverse(X)),
inference(substitution,[status(thm)],[c299]) ).
cnf(c301,plain,
double_divide(X2,inverse(X)) = inverse(multiply(inverse(X),X2)),
inference(symmetry,[status(thm)],[c300]) ).
cnf(c302,plain,
double_divide(identity,double_divide(X2,inverse(X))) = double_divide(identity,inverse(multiply(inverse(X),X2))),
inference(congruence,[status(thm)],[c301]) ).
cnf(c303,plain,
double_divide(identity,inverse(multiply(inverse(X),X2))) = multiply(multiply(inverse(X),X2),identity),
inference(substitution,[status(thm)],[c145]) ).
cnf(c304,plain,
multiply(multiply(inverse(X),X2),identity) = multiply(inverse(X),X2),
inference(substitution,[status(thm)],[c174]) ).
cnf(c305,plain,
double_divide(identity,inverse(multiply(inverse(X),X2))) = multiply(inverse(X),X2),
inference(transitivity,[status(thm)],[c303,c304]) ).
cnf(c306,plain,
double_divide(identity,double_divide(X2,inverse(X))) = multiply(inverse(X),X2),
inference(transitivity,[status(thm)],[c302,c305]) ).
cnf(c307,plain,
double_divide(identity,double_divide(inverse(X2),inverse(X))) = multiply(inverse(X),inverse(X2)),
inference(substitution,[status(thm)],[c306]) ).
cnf(c308,plain,
multiply(inverse(X),inverse(X2)) = double_divide(identity,double_divide(inverse(X2),inverse(X))),
inference(symmetry,[status(thm)],[c307]) ).
cnf(c309,plain,
multiply(X,multiply(inverse(X),inverse(X2))) = multiply(X,double_divide(identity,double_divide(inverse(X2),inverse(X)))),
inference(congruence,[status(thm)],[c308]) ).
cnf(c310,plain,
double_divide(X2,multiply(X,multiply(inverse(X),inverse(X2)))) = double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),inverse(X))))),
inference(congruence,[status(thm)],[c309]) ).
cnf(c311,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c312,plain,
double_divide(inverse(X2),inverse(X)) = double_divide(inverse(X2),double_divide(X,identity)),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
double_divide(identity,double_divide(inverse(X2),inverse(X))) = double_divide(identity,double_divide(inverse(X2),double_divide(X,identity))),
inference(congruence,[status(thm)],[c312]) ).
cnf(c314,plain,
multiply(X,double_divide(identity,double_divide(inverse(X2),inverse(X)))) = multiply(X,double_divide(identity,double_divide(inverse(X2),double_divide(X,identity)))),
inference(congruence,[status(thm)],[c313]) ).
cnf(c315,plain,
double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),inverse(X))))) = double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),double_divide(X,identity))))),
inference(congruence,[status(thm)],[c314]) ).
cnf(c316,plain,
double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),double_divide(X,identity))))) = identity,
inference(substitution,[status(thm)],[c40]) ).
cnf(c317,plain,
double_divide(X2,multiply(X,double_divide(identity,double_divide(inverse(X2),inverse(X))))) = identity,
inference(transitivity,[status(thm)],[c315,c316]) ).
cnf(c318,plain,
double_divide(X2,multiply(X,multiply(inverse(X),inverse(X2)))) = identity,
inference(transitivity,[status(thm)],[c310,c317]) ).
cnf(c319,plain,
double_divide(X,multiply(X2,multiply(inverse(X2),inverse(X)))) = identity,
inference(substitution,[status(thm)],[c318]) ).
cnf(c320,plain,
double_divide(inverse(X),double_divide(X2,multiply(X3,multiply(inverse(X3),inverse(X2))))) = double_divide(inverse(X),identity),
inference(congruence,[status(thm)],[c319]) ).
cnf(c321,plain,
double_divide(identity,double_divide(inverse(X),double_divide(X2,multiply(X3,multiply(inverse(X3),inverse(X2)))))) = double_divide(identity,double_divide(inverse(X),identity)),
inference(congruence,[status(thm)],[c320]) ).
cnf(c322,plain,
multiply(X2,double_divide(identity,double_divide(inverse(X),double_divide(X2,multiply(X3,multiply(inverse(X3),inverse(X2))))))) = multiply(X2,double_divide(identity,double_divide(inverse(X),identity))),
inference(congruence,[status(thm)],[c321]) ).
cnf(c323,plain,
double_divide(X,multiply(X2,double_divide(identity,double_divide(inverse(X),double_divide(X2,multiply(X3,multiply(inverse(X3),inverse(X2)))))))) = double_divide(X,multiply(X2,double_divide(identity,double_divide(inverse(X),identity)))),
inference(congruence,[status(thm)],[c322]) ).
cnf(c324,plain,
inverse(inverse(X)) = double_divide(inverse(X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c325,plain,
double_divide(inverse(X),identity) = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c324]) ).
cnf(c326,plain,
double_divide(identity,double_divide(inverse(X),identity)) = double_divide(identity,inverse(inverse(X))),
inference(congruence,[status(thm)],[c325]) ).
cnf(c327,plain,
multiply(X2,double_divide(identity,double_divide(inverse(X),identity))) = multiply(X2,double_divide(identity,inverse(inverse(X)))),
inference(congruence,[status(thm)],[c326]) ).
cnf(c328,plain,
double_divide(X,multiply(X2,double_divide(identity,double_divide(inverse(X),identity)))) = double_divide(X,multiply(X2,double_divide(identity,inverse(inverse(X))))),
inference(congruence,[status(thm)],[c327]) ).
cnf(c329,plain,
double_divide(X,multiply(X2,double_divide(identity,inverse(inverse(X))))) = inverse(X2),
inference(substitution,[status(thm)],[c43]) ).
cnf(c330,plain,
double_divide(X,multiply(X2,double_divide(identity,double_divide(inverse(X),identity)))) = inverse(X2),
inference(transitivity,[status(thm)],[c328,c329]) ).
cnf(c331,plain,
double_divide(X,multiply(X2,double_divide(identity,double_divide(inverse(X),double_divide(X2,multiply(X3,multiply(inverse(X3),inverse(X2)))))))) = inverse(X2),
inference(transitivity,[status(thm)],[c323,c330]) ).
cnf(c332,plain,
multiply(X2,multiply(inverse(X2),inverse(X))) = inverse(X),
inference(transitivity,[status(thm)],[c263,c331]) ).
cnf(c333,plain,
multiply(inverse(X2),multiply(inverse(inverse(X2)),inverse(X))) = inverse(X),
inference(substitution,[status(thm)],[c332]) ).
cnf(c334,plain,
multiply(inverse(X2),multiply(X2,inverse(inverse(inverse(X))))) = inverse(X),
inference(transitivity,[status(thm)],[c261,c333]) ).
cnf(c335,plain,
multiply(inverse(X2),multiply(X2,inverse(X))) = inverse(X),
inference(transitivity,[status(thm)],[c258,c334]) ).
cnf(c336,plain,
multiply(inverse(X),multiply(X,inverse(X2))) = inverse(X2),
inference(substitution,[status(thm)],[c335]) ).
cnf(c337,plain,
inverse(X2) = multiply(inverse(X),multiply(X,inverse(X2))),
inference(symmetry,[status(thm)],[c336]) ).
cnf(c338,plain,
multiply(inverse(X2),inverse(multiply(X,inverse(X2)))) = multiply(multiply(inverse(X),multiply(X,inverse(X2))),inverse(multiply(X,inverse(X2)))),
inference(congruence,[status(thm)],[c337]) ).
cnf(c339,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c340,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c339]) ).
cnf(c341,plain,
inverse(multiply(X2,X)) = inverse(inverse(double_divide(X,X2))),
inference(congruence,[status(thm)],[c340]) ).
cnf(c342,plain,
multiply(multiply(X3,multiply(X2,X)),inverse(multiply(X2,X))) = multiply(multiply(X3,multiply(X2,X)),inverse(inverse(double_divide(X,X2)))),
inference(congruence,[status(thm)],[c341]) ).
cnf(c343,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c344,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c343]) ).
cnf(c345,plain,
multiply(X3,multiply(X2,X)) = multiply(X3,inverse(double_divide(X,X2))),
inference(congruence,[status(thm)],[c344]) ).
cnf(c346,plain,
multiply(multiply(X3,multiply(X2,X)),inverse(inverse(double_divide(X,X2)))) = multiply(multiply(X3,inverse(double_divide(X,X2))),inverse(inverse(double_divide(X,X2)))),
inference(congruence,[status(thm)],[c345]) ).
cnf(c347,plain,
inverse(inverse(X)) = multiply(X,identity),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c348,plain,
multiply(multiply(X2,inverse(X)),inverse(inverse(X))) = multiply(multiply(X2,inverse(X)),multiply(X,identity)),
inference(congruence,[status(thm)],[c347]) ).
cnf(c349,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c350,plain,
multiply(X,identity) = multiply(X,inverse(identity)),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
multiply(multiply(X2,inverse(X)),multiply(X,identity)) = multiply(multiply(X2,inverse(X)),multiply(X,inverse(identity))),
inference(congruence,[status(thm)],[c350]) ).
cnf(c352,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c353,plain,
inverse(identity) = inverse(inverse(identity)),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
multiply(X,inverse(identity)) = multiply(X,inverse(inverse(identity))),
inference(congruence,[status(thm)],[c353]) ).
cnf(c355,plain,
multiply(multiply(X2,inverse(X)),multiply(X,inverse(identity))) = multiply(multiply(X2,inverse(X)),multiply(X,inverse(inverse(identity)))),
inference(congruence,[status(thm)],[c354]) ).
cnf(c356,plain,
multiply(inverse(inverse(X)),identity) = multiply(X,inverse(inverse(identity))),
inference(substitution,[status(thm)],[c222]) ).
cnf(c357,plain,
multiply(X,inverse(inverse(identity))) = multiply(inverse(inverse(X)),identity),
inference(symmetry,[status(thm)],[c356]) ).
cnf(c358,plain,
multiply(multiply(X2,inverse(X)),multiply(X,inverse(inverse(identity)))) = multiply(multiply(X2,inverse(X)),multiply(inverse(inverse(X)),identity)),
inference(congruence,[status(thm)],[c357]) ).
cnf(c359,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c360,plain,
multiply(X2,inverse(X)) = multiply(X2,double_divide(X,identity)),
inference(congruence,[status(thm)],[c359]) ).
cnf(c361,plain,
multiply(multiply(X2,inverse(X)),multiply(inverse(inverse(X)),identity)) = multiply(multiply(X2,double_divide(X,identity)),multiply(inverse(inverse(X)),identity)),
inference(congruence,[status(thm)],[c360]) ).
cnf(c362,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c363,plain,
double_divide(X,identity) = double_divide(X,inverse(identity)),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
multiply(X2,double_divide(X,identity)) = multiply(X2,double_divide(X,inverse(identity))),
inference(congruence,[status(thm)],[c363]) ).
cnf(c365,plain,
multiply(multiply(X2,double_divide(X,identity)),multiply(inverse(inverse(X)),identity)) = multiply(multiply(X2,double_divide(X,inverse(identity))),multiply(inverse(inverse(X)),identity)),
inference(congruence,[status(thm)],[c364]) ).
cnf(c366,plain,
double_divide(X,inverse(identity)) = inverse(multiply(inverse(inverse(X)),identity)),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c367,plain,
multiply(X2,double_divide(X,inverse(identity))) = multiply(X2,inverse(multiply(inverse(inverse(X)),identity))),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
multiply(multiply(X2,double_divide(X,inverse(identity))),multiply(inverse(inverse(X)),identity)) = multiply(multiply(X2,inverse(multiply(inverse(inverse(X)),identity))),multiply(inverse(inverse(X)),identity)),
inference(congruence,[status(thm)],[c367]) ).
cnf(c369,plain,
multiply(multiply(X2,inverse(multiply(inverse(inverse(X)),identity))),multiply(inverse(inverse(X)),identity)) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c215]) ).
cnf(c370,plain,
multiply(multiply(X2,double_divide(X,inverse(identity))),multiply(inverse(inverse(X)),identity)) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c368,c369]) ).
cnf(c371,plain,
multiply(multiply(X2,double_divide(X,identity)),multiply(inverse(inverse(X)),identity)) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c365,c370]) ).
cnf(c372,plain,
multiply(multiply(X2,inverse(X)),multiply(inverse(inverse(X)),identity)) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c361,c371]) ).
cnf(c373,plain,
multiply(multiply(X2,inverse(X)),multiply(X,inverse(inverse(identity)))) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c358,c372]) ).
cnf(c374,plain,
multiply(multiply(X2,inverse(X)),multiply(X,inverse(identity))) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c355,c373]) ).
cnf(c375,plain,
multiply(multiply(X2,inverse(X)),multiply(X,identity)) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c351,c374]) ).
cnf(c376,plain,
multiply(multiply(X2,inverse(X)),inverse(inverse(X))) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c348,c375]) ).
cnf(c377,plain,
multiply(multiply(X3,inverse(double_divide(X,X2))),inverse(inverse(double_divide(X,X2)))) = inverse(inverse(X3)),
inference(substitution,[status(thm)],[c376]) ).
cnf(c378,plain,
multiply(multiply(X3,multiply(X2,X)),inverse(inverse(double_divide(X,X2)))) = inverse(inverse(X3)),
inference(transitivity,[status(thm)],[c346,c377]) ).
cnf(c379,plain,
multiply(multiply(X3,multiply(X2,X)),inverse(multiply(X2,X))) = inverse(inverse(X3)),
inference(transitivity,[status(thm)],[c342,c378]) ).
cnf(c380,plain,
multiply(multiply(inverse(X),multiply(X,inverse(X2))),inverse(multiply(X,inverse(X2)))) = inverse(inverse(inverse(X))),
inference(substitution,[status(thm)],[c379]) ).
cnf(c381,plain,
multiply(multiply(inverse(X),multiply(X,inverse(X2))),inverse(multiply(X,inverse(X2)))) = inverse(X),
inference(transitivity,[status(thm)],[c380,c193]) ).
cnf(c382,plain,
multiply(inverse(X2),inverse(multiply(X,inverse(X2)))) = inverse(X),
inference(transitivity,[status(thm)],[c338,c381]) ).
cnf(c383,plain,
multiply(inverse(X2),double_divide(inverse(X2),X)) = inverse(X),
inference(transitivity,[status(thm)],[c255,c382]) ).
cnf(c384,plain,
multiply(inverse(X),double_divide(inverse(X),double_divide(identity,X2))) = inverse(double_divide(identity,X2)),
inference(substitution,[status(thm)],[c383]) ).
cnf(c385,plain,
inverse(double_divide(identity,X2)) = multiply(inverse(X),double_divide(inverse(X),double_divide(identity,X2))),
inference(symmetry,[status(thm)],[c384]) ).
cnf(c386,plain,
multiply(inverse(X),inverse(inverse(double_divide(inverse(X),double_divide(identity,X2))))) = multiply(inverse(X),double_divide(inverse(X),double_divide(identity,X2))),
inference(substitution,[status(thm)],[c251]) ).
cnf(c387,plain,
multiply(inverse(X),double_divide(inverse(X),double_divide(identity,X2))) = multiply(inverse(X),inverse(inverse(double_divide(inverse(X),double_divide(identity,X2))))),
inference(symmetry,[status(thm)],[c386]) ).
cnf(c388,plain,
multiply(double_divide(inverse(X),double_divide(identity,X2)),identity) = inverse(inverse(double_divide(inverse(X),double_divide(identity,X2)))),
inference(substitution,[status(thm)],[c177]) ).
cnf(c389,plain,
inverse(inverse(double_divide(inverse(X),double_divide(identity,X2)))) = multiply(double_divide(inverse(X),double_divide(identity,X2)),identity),
inference(symmetry,[status(thm)],[c388]) ).
cnf(c390,plain,
multiply(inverse(X),inverse(inverse(double_divide(inverse(X),double_divide(identity,X2))))) = multiply(inverse(X),multiply(double_divide(inverse(X),double_divide(identity,X2)),identity)),
inference(congruence,[status(thm)],[c389]) ).
cnf(c391,plain,
inverse(double_divide(identity,double_divide(inverse(X),double_divide(identity,X2)))) = multiply(double_divide(inverse(X),double_divide(identity,X2)),identity),
inference(substitution,[status(thm)],[c13]) ).
cnf(c392,plain,
multiply(double_divide(inverse(X),double_divide(identity,X2)),identity) = inverse(double_divide(identity,double_divide(inverse(X),double_divide(identity,X2)))),
inference(symmetry,[status(thm)],[c391]) ).
cnf(c393,plain,
multiply(inverse(X),multiply(double_divide(inverse(X),double_divide(identity,X2)),identity)) = multiply(inverse(X),inverse(double_divide(identity,double_divide(inverse(X),double_divide(identity,X2))))),
inference(congruence,[status(thm)],[c392]) ).
cnf(c394,plain,
inverse(X) = inverse(inverse(inverse(X))),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c395,plain,
double_divide(X2,inverse(X)) = double_divide(X2,inverse(inverse(inverse(X)))),
inference(congruence,[status(thm)],[c394]) ).
cnf(c396,plain,
multiply(inverse(X),identity) = inverse(inverse(inverse(X))),
inference(substitution,[status(thm)],[c177]) ).
cnf(c397,plain,
inverse(inverse(inverse(X))) = multiply(inverse(X),identity),
inference(symmetry,[status(thm)],[c396]) ).
cnf(c398,plain,
double_divide(X2,inverse(inverse(inverse(X)))) = double_divide(X2,multiply(inverse(X),identity)),
inference(congruence,[status(thm)],[c397]) ).
cnf(c399,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c400,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c399]) ).
cnf(c401,plain,
multiply(multiply(X3,X2),X) = multiply(inverse(double_divide(X2,X3)),X),
inference(congruence,[status(thm)],[c400]) ).
cnf(c402,plain,
inverse(multiply(multiply(X3,X2),X)) = inverse(multiply(inverse(double_divide(X2,X3)),X)),
inference(congruence,[status(thm)],[c401]) ).
cnf(c403,plain,
inverse(multiply(inverse(double_divide(X2,X3)),X)) = double_divide(X,inverse(double_divide(X2,X3))),
inference(substitution,[status(thm)],[c299]) ).
cnf(c404,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c405,plain,
double_divide(X,inverse(double_divide(X2,X3))) = double_divide(X,multiply(X3,X2)),
inference(congruence,[status(thm)],[c404]) ).
cnf(c406,plain,
inverse(multiply(inverse(double_divide(X2,X3)),X)) = double_divide(X,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c403,c405]) ).
cnf(c407,plain,
inverse(multiply(multiply(X3,X2),X)) = double_divide(X,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c402,c406]) ).
cnf(c408,plain,
inverse(multiply(multiply(inverse(X),identity),X2)) = double_divide(X2,multiply(inverse(X),identity)),
inference(substitution,[status(thm)],[c407]) ).
cnf(c409,plain,
double_divide(X2,multiply(inverse(X),identity)) = inverse(multiply(multiply(inverse(X),identity),X2)),
inference(symmetry,[status(thm)],[c408]) ).
cnf(c410,plain,
double_divide(identity,inverse(inverse(X))) = multiply(inverse(X),identity),
inference(substitution,[status(thm)],[c145]) ).
cnf(c411,plain,
multiply(inverse(X),identity) = double_divide(identity,inverse(inverse(X))),
inference(symmetry,[status(thm)],[c410]) ).
cnf(c412,plain,
multiply(multiply(inverse(X),identity),X2) = multiply(double_divide(identity,inverse(inverse(X))),X2),
inference(congruence,[status(thm)],[c411]) ).
cnf(c413,plain,
inverse(multiply(multiply(inverse(X),identity),X2)) = inverse(multiply(double_divide(identity,inverse(inverse(X))),X2)),
inference(congruence,[status(thm)],[c412]) ).
cnf(c414,plain,
double_divide(identity,inverse(inverse(X))) = inverse(multiply(X,identity)),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c415,plain,
multiply(double_divide(identity,inverse(inverse(X))),X2) = multiply(inverse(multiply(X,identity)),X2),
inference(congruence,[status(thm)],[c414]) ).
cnf(c416,plain,
inverse(multiply(double_divide(identity,inverse(inverse(X))),X2)) = inverse(multiply(inverse(multiply(X,identity)),X2)),
inference(congruence,[status(thm)],[c415]) ).
cnf(c417,plain,
multiply(inverse(X),double_divide(inverse(X),multiply(inverse(X2),X))) = inverse(multiply(inverse(X2),X)),
inference(substitution,[status(thm)],[c383]) ).
cnf(c418,plain,
inverse(multiply(inverse(X2),X)) = multiply(inverse(X),double_divide(inverse(X),multiply(inverse(X2),X))),
inference(symmetry,[status(thm)],[c417]) ).
cnf(c419,plain,
multiply(inverse(X),inverse(inverse(X2))) = multiply(inverse(X),X2),
inference(substitution,[status(thm)],[c251]) ).
cnf(c420,plain,
multiply(inverse(X),X2) = multiply(inverse(X),inverse(inverse(X2))),
inference(symmetry,[status(thm)],[c419]) ).
cnf(c421,plain,
double_divide(inverse(X2),multiply(inverse(X),X2)) = double_divide(inverse(X2),multiply(inverse(X),inverse(inverse(X2)))),
inference(congruence,[status(thm)],[c420]) ).
cnf(c422,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c423,plain,
multiply(X,inverse(X2)) = multiply(X,double_divide(X2,identity)),
inference(congruence,[status(thm)],[c422]) ).
cnf(c424,plain,
double_divide(X2,multiply(X,inverse(X2))) = double_divide(X2,multiply(X,double_divide(X2,identity))),
inference(congruence,[status(thm)],[c423]) ).
cnf(c425,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c426,plain,
double_divide(X,identity) = double_divide(X,inverse(identity)),
inference(congruence,[status(thm)],[c425]) ).
cnf(c427,plain,
multiply(X,double_divide(X2,identity)) = multiply(X,double_divide(X2,inverse(identity))),
inference(congruence,[status(thm)],[c426]) ).
cnf(c428,plain,
double_divide(X2,multiply(X,double_divide(X2,identity))) = double_divide(X2,multiply(X,double_divide(X2,inverse(identity)))),
inference(congruence,[status(thm)],[c427]) ).
cnf(c429,plain,
double_divide(X,inverse(identity)) = inverse(multiply(inverse(inverse(X)),identity)),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c430,plain,
multiply(X,double_divide(X2,inverse(identity))) = multiply(X,inverse(multiply(inverse(inverse(X2)),identity))),
inference(congruence,[status(thm)],[c429]) ).
cnf(c431,plain,
double_divide(X2,multiply(X,double_divide(X2,inverse(identity)))) = double_divide(X2,multiply(X,inverse(multiply(inverse(inverse(X2)),identity)))),
inference(congruence,[status(thm)],[c430]) ).
cnf(c432,plain,
inverse(double_divide(identity,inverse(inverse(X)))) = multiply(inverse(inverse(X)),identity),
inference(substitution,[status(thm)],[c13]) ).
cnf(c433,plain,
multiply(inverse(inverse(X)),identity) = inverse(double_divide(identity,inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c432]) ).
cnf(c434,plain,
inverse(multiply(inverse(inverse(X)),identity)) = inverse(inverse(double_divide(identity,inverse(inverse(X))))),
inference(congruence,[status(thm)],[c433]) ).
cnf(c435,plain,
multiply(X,inverse(multiply(inverse(inverse(X2)),identity))) = multiply(X,inverse(inverse(double_divide(identity,inverse(inverse(X2)))))),
inference(congruence,[status(thm)],[c434]) ).
cnf(c436,plain,
double_divide(X2,multiply(X,inverse(multiply(inverse(inverse(X2)),identity)))) = double_divide(X2,multiply(X,inverse(inverse(double_divide(identity,inverse(inverse(X2))))))),
inference(congruence,[status(thm)],[c435]) ).
cnf(c437,plain,
multiply(inverse(inverse(X)),double_divide(identity,inverse(inverse(X2)))) = multiply(X,inverse(inverse(double_divide(identity,inverse(inverse(X2)))))),
inference(substitution,[status(thm)],[c222]) ).
cnf(c438,plain,
multiply(X,inverse(inverse(double_divide(identity,inverse(inverse(X2)))))) = multiply(inverse(inverse(X)),double_divide(identity,inverse(inverse(X2)))),
inference(symmetry,[status(thm)],[c437]) ).
cnf(c439,plain,
double_divide(X2,multiply(X,inverse(inverse(double_divide(identity,inverse(inverse(X2))))))) = double_divide(X2,multiply(inverse(inverse(X)),double_divide(identity,inverse(inverse(X2))))),
inference(congruence,[status(thm)],[c438]) ).
cnf(c440,plain,
double_divide(X2,multiply(inverse(inverse(X)),double_divide(identity,inverse(inverse(X2))))) = inverse(inverse(inverse(X))),
inference(substitution,[status(thm)],[c43]) ).
cnf(c441,plain,
double_divide(X2,multiply(inverse(inverse(X)),double_divide(identity,inverse(inverse(X2))))) = inverse(X),
inference(transitivity,[status(thm)],[c440,c193]) ).
cnf(c442,plain,
double_divide(X2,multiply(X,inverse(inverse(double_divide(identity,inverse(inverse(X2))))))) = inverse(X),
inference(transitivity,[status(thm)],[c439,c441]) ).
cnf(c443,plain,
double_divide(X2,multiply(X,inverse(multiply(inverse(inverse(X2)),identity)))) = inverse(X),
inference(transitivity,[status(thm)],[c436,c442]) ).
cnf(c444,plain,
double_divide(X2,multiply(X,double_divide(X2,inverse(identity)))) = inverse(X),
inference(transitivity,[status(thm)],[c431,c443]) ).
cnf(c445,plain,
double_divide(X2,multiply(X,double_divide(X2,identity))) = inverse(X),
inference(transitivity,[status(thm)],[c428,c444]) ).
cnf(c446,plain,
double_divide(X2,multiply(X,inverse(X2))) = inverse(X),
inference(transitivity,[status(thm)],[c424,c445]) ).
cnf(c447,plain,
double_divide(inverse(X2),multiply(inverse(X),inverse(inverse(X2)))) = inverse(inverse(X)),
inference(substitution,[status(thm)],[c446]) ).
cnf(c448,plain,
double_divide(inverse(X2),multiply(inverse(X),X2)) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c421,c447]) ).
cnf(c449,plain,
double_divide(inverse(X),multiply(inverse(X2),X)) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c448]) ).
cnf(c450,plain,
multiply(inverse(X),double_divide(inverse(X),multiply(inverse(X2),X))) = multiply(inverse(X),inverse(inverse(X2))),
inference(congruence,[status(thm)],[c449]) ).
cnf(c451,plain,
multiply(inverse(X),inverse(inverse(X2))) = multiply(inverse(X),X2),
inference(substitution,[status(thm)],[c251]) ).
cnf(c452,plain,
multiply(inverse(X),double_divide(inverse(X),multiply(inverse(X2),X))) = multiply(inverse(X),X2),
inference(transitivity,[status(thm)],[c450,c451]) ).
cnf(c453,plain,
inverse(multiply(inverse(X2),X)) = multiply(inverse(X),X2),
inference(transitivity,[status(thm)],[c418,c452]) ).
cnf(c454,plain,
inverse(multiply(inverse(multiply(X,identity)),X2)) = multiply(inverse(X2),multiply(X,identity)),
inference(substitution,[status(thm)],[c453]) ).
cnf(c455,plain,
multiply(inverse(X2),multiply(X,identity)) = multiply(inverse(X2),inverse(inverse(X))),
inference(congruence,[status(thm)],[c177]) ).
cnf(c456,plain,
multiply(inverse(X2),multiply(X,identity)) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c455,c251]) ).
cnf(c457,plain,
inverse(multiply(inverse(multiply(X,identity)),X2)) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c454,c456]) ).
cnf(c458,plain,
inverse(multiply(double_divide(identity,inverse(inverse(X))),X2)) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c416,c457]) ).
cnf(c459,plain,
inverse(multiply(multiply(inverse(X),identity),X2)) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c413,c458]) ).
cnf(c460,plain,
double_divide(X2,multiply(inverse(X),identity)) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c409,c459]) ).
cnf(c461,plain,
double_divide(X2,inverse(inverse(inverse(X)))) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c398,c460]) ).
cnf(c462,plain,
double_divide(X2,inverse(X)) = multiply(inverse(X2),X),
inference(transitivity,[status(thm)],[c395,c461]) ).
cnf(c463,plain,
double_divide(X,inverse(inverse(double_divide(identity,double_divide(inverse(X),double_divide(identity,X2)))))) = multiply(inverse(X),inverse(double_divide(identity,double_divide(inverse(X),double_divide(identity,X2))))),
inference(substitution,[status(thm)],[c462]) ).
cnf(c464,plain,
multiply(inverse(X),inverse(double_divide(identity,double_divide(inverse(X),double_divide(identity,X2))))) = double_divide(X,inverse(inverse(double_divide(identity,double_divide(inverse(X),double_divide(identity,X2)))))),
inference(symmetry,[status(thm)],[c463]) ).
cnf(c465,plain,
multiply(identity,double_divide(identity,double_divide(inverse(X),double_divide(identity,X2)))) = inverse(inverse(double_divide(identity,double_divide(inverse(X),double_divide(identity,X2))))),
inference(substitution,[status(thm)],[c67]) ).
cnf(c466,plain,
inverse(inverse(double_divide(identity,double_divide(inverse(X),double_divide(identity,X2))))) = multiply(identity,double_divide(identity,double_divide(inverse(X),double_divide(identity,X2)))),
inference(symmetry,[status(thm)],[c465]) ).
cnf(c467,plain,
double_divide(X,inverse(inverse(double_divide(identity,double_divide(inverse(X),double_divide(identity,X2)))))) = double_divide(X,multiply(identity,double_divide(identity,double_divide(inverse(X),double_divide(identity,X2))))),
inference(congruence,[status(thm)],[c466]) ).
cnf(c468,plain,
double_divide(X,multiply(identity,double_divide(identity,double_divide(inverse(X),double_divide(identity,X2))))) = X2,
inference(substitution,[status(thm)],[c40]) ).
cnf(c469,plain,
double_divide(X,inverse(inverse(double_divide(identity,double_divide(inverse(X),double_divide(identity,X2)))))) = X2,
inference(transitivity,[status(thm)],[c467,c468]) ).
cnf(c470,plain,
multiply(inverse(X),inverse(double_divide(identity,double_divide(inverse(X),double_divide(identity,X2))))) = X2,
inference(transitivity,[status(thm)],[c464,c469]) ).
cnf(c471,plain,
multiply(inverse(X),multiply(double_divide(inverse(X),double_divide(identity,X2)),identity)) = X2,
inference(transitivity,[status(thm)],[c393,c470]) ).
cnf(c472,plain,
multiply(inverse(X),inverse(inverse(double_divide(inverse(X),double_divide(identity,X2))))) = X2,
inference(transitivity,[status(thm)],[c390,c471]) ).
cnf(c473,plain,
multiply(inverse(X),double_divide(inverse(X),double_divide(identity,X2))) = X2,
inference(transitivity,[status(thm)],[c387,c472]) ).
cnf(c474,plain,
inverse(double_divide(identity,X)) = X,
inference(transitivity,[status(thm)],[c385,c473]) ).
cnf(c475,plain,
multiply(X,identity) = X,
inference(transitivity,[status(thm)],[c180,c474]) ).
cnf(c476,plain,
inverse(inverse(X)) = X,
inference(transitivity,[status(thm)],[c178,c475]) ).
cnf(c477,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c476]) ).
cnf(c478,plain,
multiply(X2,X) = multiply(X2,inverse(inverse(X))),
inference(congruence,[status(thm)],[c477]) ).
cnf(c479,plain,
multiply(X3,multiply(X2,X)) = multiply(X3,multiply(X2,inverse(inverse(X)))),
inference(congruence,[status(thm)],[c478]) ).
cnf(c480,plain,
multiply(multiply(X3,multiply(X2,X)),inverse(X)) = multiply(multiply(X3,multiply(X2,inverse(inverse(X)))),inverse(X)),
inference(congruence,[status(thm)],[c479]) ).
cnf(c481,plain,
multiply(X2,inverse(inverse(X))) = multiply(inverse(inverse(X2)),X),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c482,plain,
multiply(X3,multiply(X2,inverse(inverse(X)))) = multiply(X3,multiply(inverse(inverse(X2)),X)),
inference(congruence,[status(thm)],[c481]) ).
cnf(c483,plain,
multiply(multiply(X3,multiply(X2,inverse(inverse(X)))),inverse(X)) = multiply(multiply(X3,multiply(inverse(inverse(X2)),X)),inverse(X)),
inference(congruence,[status(thm)],[c482]) ).
cnf(c484,plain,
inverse(multiply(inverse(X),inverse(X2))) = multiply(inverse(inverse(X2)),X),
inference(substitution,[status(thm)],[c453]) ).
cnf(c485,plain,
multiply(inverse(inverse(X2)),X) = inverse(multiply(inverse(X),inverse(X2))),
inference(symmetry,[status(thm)],[c484]) ).
cnf(c486,plain,
multiply(X3,multiply(inverse(inverse(X2)),X)) = multiply(X3,inverse(multiply(inverse(X),inverse(X2)))),
inference(congruence,[status(thm)],[c485]) ).
cnf(c487,plain,
multiply(multiply(X3,multiply(inverse(inverse(X2)),X)),inverse(X)) = multiply(multiply(X3,inverse(multiply(inverse(X),inverse(X2)))),inverse(X)),
inference(congruence,[status(thm)],[c486]) ).
cnf(c488,plain,
multiply(inverse(inverse(multiply(X3,X2))),X) = multiply(multiply(X3,X2),inverse(inverse(X))),
inference(substitution,[status(thm)],[c222]) ).
cnf(c489,plain,
multiply(multiply(X3,X2),inverse(inverse(X))) = multiply(inverse(inverse(multiply(X3,X2))),X),
inference(symmetry,[status(thm)],[c488]) ).
cnf(c490,plain,
multiply(inverse(inverse(multiply(X3,X2))),X) = multiply(multiply(X3,X2),X),
inference(congruence,[status(thm)],[c169]) ).
cnf(c491,plain,
multiply(multiply(X3,X2),inverse(inverse(X))) = multiply(multiply(X3,X2),X),
inference(transitivity,[status(thm)],[c489,c490]) ).
cnf(c492,plain,
multiply(multiply(X3,inverse(multiply(inverse(X),inverse(X2)))),inverse(inverse(inverse(X)))) = multiply(multiply(X3,inverse(multiply(inverse(X),inverse(X2)))),inverse(X)),
inference(substitution,[status(thm)],[c491]) ).
cnf(c493,plain,
multiply(multiply(X3,inverse(multiply(inverse(X),inverse(X2)))),inverse(X)) = multiply(multiply(X3,inverse(multiply(inverse(X),inverse(X2)))),inverse(inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c492]) ).
cnf(c494,plain,
inverse(X) = inverse(inverse(inverse(X))),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c495,plain,
double_divide(inverse(X2),X) = double_divide(inverse(inverse(inverse(X2))),X),
inference(congruence,[status(thm)],[c494]) ).
cnf(c496,plain,
multiply(inverse(X),identity) = inverse(inverse(inverse(X))),
inference(substitution,[status(thm)],[c177]) ).
cnf(c497,plain,
inverse(inverse(inverse(X))) = multiply(inverse(X),identity),
inference(symmetry,[status(thm)],[c496]) ).
cnf(c498,plain,
double_divide(inverse(inverse(inverse(X2))),X) = double_divide(multiply(inverse(X2),identity),X),
inference(congruence,[status(thm)],[c497]) ).
cnf(c499,plain,
double_divide(identity,inverse(inverse(X))) = multiply(inverse(X),identity),
inference(substitution,[status(thm)],[c145]) ).
cnf(c500,plain,
multiply(inverse(X),identity) = double_divide(identity,inverse(inverse(X))),
inference(symmetry,[status(thm)],[c499]) ).
cnf(c501,plain,
double_divide(multiply(inverse(X2),identity),X) = double_divide(double_divide(identity,inverse(inverse(X2))),X),
inference(congruence,[status(thm)],[c500]) ).
cnf(c502,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c503,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c502]) ).
cnf(c504,plain,
inverse(multiply(X2,X)) = inverse(inverse(double_divide(X,X2))),
inference(congruence,[status(thm)],[c503]) ).
cnf(c505,plain,
inverse(inverse(double_divide(X,X2))) = double_divide(X,X2),
inference(substitution,[status(thm)],[c476]) ).
cnf(c506,plain,
inverse(multiply(X2,X)) = double_divide(X,X2),
inference(transitivity,[status(thm)],[c504,c505]) ).
cnf(c507,plain,
inverse(multiply(X,double_divide(identity,inverse(inverse(X2))))) = double_divide(double_divide(identity,inverse(inverse(X2))),X),
inference(substitution,[status(thm)],[c506]) ).
cnf(c508,plain,
double_divide(double_divide(identity,inverse(inverse(X2))),X) = inverse(multiply(X,double_divide(identity,inverse(inverse(X2))))),
inference(symmetry,[status(thm)],[c507]) ).
cnf(c509,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c476]) ).
cnf(c510,plain,
double_divide(X2,X) = double_divide(inverse(inverse(X2)),X),
inference(congruence,[status(thm)],[c509]) ).
cnf(c511,plain,
multiply(X2,double_divide(X2,X)) = multiply(X2,double_divide(inverse(inverse(X2)),X)),
inference(congruence,[status(thm)],[c510]) ).
cnf(c512,plain,
inverse(inverse(X)) = multiply(X,identity),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c513,plain,
double_divide(inverse(inverse(X2)),X) = double_divide(multiply(X2,identity),X),
inference(congruence,[status(thm)],[c512]) ).
cnf(c514,plain,
multiply(X2,double_divide(inverse(inverse(X2)),X)) = multiply(X2,double_divide(multiply(X2,identity),X)),
inference(congruence,[status(thm)],[c513]) ).
cnf(c515,plain,
multiply(X,identity) = double_divide(identity,inverse(X)),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c516,plain,
double_divide(multiply(X2,identity),X) = double_divide(double_divide(identity,inverse(X2)),X),
inference(congruence,[status(thm)],[c515]) ).
cnf(c517,plain,
multiply(X2,double_divide(multiply(X2,identity),X)) = multiply(X2,double_divide(double_divide(identity,inverse(X2)),X)),
inference(congruence,[status(thm)],[c516]) ).
cnf(c518,plain,
inverse(inverse(double_divide(double_divide(identity,inverse(X2)),X))) = double_divide(double_divide(identity,inverse(X2)),X),
inference(substitution,[status(thm)],[c476]) ).
cnf(c519,plain,
double_divide(double_divide(identity,inverse(X2)),X) = inverse(inverse(double_divide(double_divide(identity,inverse(X2)),X))),
inference(symmetry,[status(thm)],[c518]) ).
cnf(c520,plain,
multiply(X2,double_divide(double_divide(identity,inverse(X2)),X)) = multiply(X2,inverse(inverse(double_divide(double_divide(identity,inverse(X2)),X)))),
inference(congruence,[status(thm)],[c519]) ).
cnf(c521,plain,
multiply(inverse(inverse(X2)),double_divide(double_divide(identity,inverse(X2)),X)) = multiply(X2,inverse(inverse(double_divide(double_divide(identity,inverse(X2)),X)))),
inference(substitution,[status(thm)],[c222]) ).
cnf(c522,plain,
multiply(X2,inverse(inverse(double_divide(double_divide(identity,inverse(X2)),X)))) = multiply(inverse(inverse(X2)),double_divide(double_divide(identity,inverse(X2)),X)),
inference(symmetry,[status(thm)],[c521]) ).
cnf(c523,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c524,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c523]) ).
cnf(c525,plain,
double_divide(X3,multiply(X2,X)) = double_divide(X3,inverse(double_divide(X,X2))),
inference(congruence,[status(thm)],[c524]) ).
cnf(c526,plain,
double_divide(X3,inverse(double_divide(X,X2))) = multiply(inverse(X3),double_divide(X,X2)),
inference(substitution,[status(thm)],[c462]) ).
cnf(c527,plain,
double_divide(X3,multiply(X2,X)) = multiply(inverse(X3),double_divide(X,X2)),
inference(transitivity,[status(thm)],[c525,c526]) ).
cnf(c528,plain,
double_divide(inverse(X2),multiply(X,double_divide(identity,inverse(X2)))) = multiply(inverse(inverse(X2)),double_divide(double_divide(identity,inverse(X2)),X)),
inference(substitution,[status(thm)],[c527]) ).
cnf(c529,plain,
multiply(inverse(inverse(X2)),double_divide(double_divide(identity,inverse(X2)),X)) = double_divide(inverse(X2),multiply(X,double_divide(identity,inverse(X2)))),
inference(symmetry,[status(thm)],[c528]) ).
cnf(c530,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c476]) ).
cnf(c531,plain,
inverse(X) = inverse(inverse(inverse(X))),
inference(congruence,[status(thm)],[c530]) ).
cnf(c532,plain,
double_divide(identity,inverse(X)) = double_divide(identity,inverse(inverse(inverse(X)))),
inference(congruence,[status(thm)],[c531]) ).
cnf(c533,plain,
multiply(X,double_divide(identity,inverse(X2))) = multiply(X,double_divide(identity,inverse(inverse(inverse(X2))))),
inference(congruence,[status(thm)],[c532]) ).
cnf(c534,plain,
double_divide(inverse(X2),multiply(X,double_divide(identity,inverse(X2)))) = double_divide(inverse(X2),multiply(X,double_divide(identity,inverse(inverse(inverse(X2)))))),
inference(congruence,[status(thm)],[c533]) ).
cnf(c535,plain,
double_divide(inverse(X2),multiply(X,double_divide(identity,inverse(inverse(inverse(X2)))))) = inverse(X),
inference(substitution,[status(thm)],[c43]) ).
cnf(c536,plain,
double_divide(inverse(X2),multiply(X,double_divide(identity,inverse(X2)))) = inverse(X),
inference(transitivity,[status(thm)],[c534,c535]) ).
cnf(c537,plain,
multiply(inverse(inverse(X2)),double_divide(double_divide(identity,inverse(X2)),X)) = inverse(X),
inference(transitivity,[status(thm)],[c529,c536]) ).
cnf(c538,plain,
multiply(X2,inverse(inverse(double_divide(double_divide(identity,inverse(X2)),X)))) = inverse(X),
inference(transitivity,[status(thm)],[c522,c537]) ).
cnf(c539,plain,
multiply(X2,double_divide(double_divide(identity,inverse(X2)),X)) = inverse(X),
inference(transitivity,[status(thm)],[c520,c538]) ).
cnf(c540,plain,
multiply(X2,double_divide(multiply(X2,identity),X)) = inverse(X),
inference(transitivity,[status(thm)],[c517,c539]) ).
cnf(c541,plain,
multiply(X2,double_divide(inverse(inverse(X2)),X)) = inverse(X),
inference(transitivity,[status(thm)],[c514,c540]) ).
cnf(c542,plain,
multiply(X2,double_divide(X2,X)) = inverse(X),
inference(transitivity,[status(thm)],[c511,c541]) ).
cnf(c543,plain,
multiply(X2,double_divide(X2,multiply(X,double_divide(identity,inverse(inverse(X2)))))) = inverse(multiply(X,double_divide(identity,inverse(inverse(X2))))),
inference(substitution,[status(thm)],[c542]) ).
cnf(c544,plain,
inverse(multiply(X,double_divide(identity,inverse(inverse(X2))))) = multiply(X2,double_divide(X2,multiply(X,double_divide(identity,inverse(inverse(X2)))))),
inference(symmetry,[status(thm)],[c543]) ).
cnf(c545,plain,
multiply(X2,double_divide(X2,multiply(X,double_divide(identity,inverse(inverse(X2)))))) = multiply(X2,inverse(X)),
inference(congruence,[status(thm)],[c43]) ).
cnf(c546,plain,
inverse(multiply(X,double_divide(identity,inverse(inverse(X2))))) = multiply(X2,inverse(X)),
inference(transitivity,[status(thm)],[c544,c545]) ).
cnf(c547,plain,
double_divide(double_divide(identity,inverse(inverse(X2))),X) = multiply(X2,inverse(X)),
inference(transitivity,[status(thm)],[c508,c546]) ).
cnf(c548,plain,
double_divide(multiply(inverse(X2),identity),X) = multiply(X2,inverse(X)),
inference(transitivity,[status(thm)],[c501,c547]) ).
cnf(c549,plain,
double_divide(inverse(inverse(inverse(X2))),X) = multiply(X2,inverse(X)),
inference(transitivity,[status(thm)],[c498,c548]) ).
cnf(c550,plain,
double_divide(inverse(X2),X) = multiply(X2,inverse(X)),
inference(transitivity,[status(thm)],[c495,c549]) ).
cnf(c551,plain,
double_divide(inverse(X3),multiply(inverse(X),inverse(X2))) = multiply(X3,inverse(multiply(inverse(X),inverse(X2)))),
inference(substitution,[status(thm)],[c550]) ).
cnf(c552,plain,
multiply(X3,inverse(multiply(inverse(X),inverse(X2)))) = double_divide(inverse(X3),multiply(inverse(X),inverse(X2))),
inference(symmetry,[status(thm)],[c551]) ).
cnf(c553,plain,
multiply(multiply(X3,inverse(multiply(inverse(X),inverse(X2)))),inverse(inverse(inverse(X)))) = multiply(double_divide(inverse(X3),multiply(inverse(X),inverse(X2))),inverse(inverse(inverse(X)))),
inference(congruence,[status(thm)],[c552]) ).
cnf(c554,plain,
multiply(inverse(multiply(multiply(inverse(X),inverse(X2)),inverse(X3))),inverse(X)) = multiply(double_divide(inverse(X3),multiply(inverse(X),inverse(X2))),inverse(inverse(inverse(X)))),
inference(substitution,[status(thm)],[c236]) ).
cnf(c555,plain,
multiply(double_divide(inverse(X3),multiply(inverse(X),inverse(X2))),inverse(inverse(inverse(X)))) = multiply(inverse(multiply(multiply(inverse(X),inverse(X2)),inverse(X3))),inverse(X)),
inference(symmetry,[status(thm)],[c554]) ).
cnf(c556,plain,
double_divide(multiply(multiply(inverse(X),inverse(X2)),inverse(X3)),inverse(inverse(X))) = multiply(inverse(multiply(multiply(inverse(X),inverse(X2)),inverse(X3))),inverse(X)),
inference(substitution,[status(thm)],[c462]) ).
cnf(c557,plain,
multiply(inverse(multiply(multiply(inverse(X),inverse(X2)),inverse(X3))),inverse(X)) = double_divide(multiply(multiply(inverse(X),inverse(X2)),inverse(X3)),inverse(inverse(X))),
inference(symmetry,[status(thm)],[c556]) ).
cnf(c558,plain,
double_divide(multiply(X2,X),multiply(multiply(X3,multiply(X2,X)),inverse(multiply(X2,X)))) = inverse(multiply(X3,multiply(X2,X))),
inference(substitution,[status(thm)],[c446]) ).
cnf(c559,plain,
inverse(multiply(X3,multiply(X2,X))) = double_divide(multiply(X2,X),multiply(multiply(X3,multiply(X2,X)),inverse(multiply(X2,X)))),
inference(symmetry,[status(thm)],[c558]) ).
cnf(c560,plain,
double_divide(multiply(X2,X),multiply(multiply(X3,multiply(X2,X)),inverse(multiply(X2,X)))) = double_divide(multiply(X2,X),inverse(inverse(X3))),
inference(congruence,[status(thm)],[c379]) ).
cnf(c561,plain,
inverse(multiply(X3,multiply(X2,X))) = double_divide(multiply(X2,X),inverse(inverse(X3))),
inference(transitivity,[status(thm)],[c559,c560]) ).
cnf(c562,plain,
inverse(multiply(X,multiply(multiply(inverse(X),inverse(X2)),inverse(X3)))) = double_divide(multiply(multiply(inverse(X),inverse(X2)),inverse(X3)),inverse(inverse(X))),
inference(substitution,[status(thm)],[c561]) ).
cnf(c563,plain,
double_divide(multiply(multiply(inverse(X),inverse(X2)),inverse(X3)),inverse(inverse(X))) = inverse(multiply(X,multiply(multiply(inverse(X),inverse(X2)),inverse(X3)))),
inference(symmetry,[status(thm)],[c562]) ).
cnf(c564,plain,
inverse(multiply(X,X2)) = double_divide(X2,X),
inference(substitution,[status(thm)],[c506]) ).
cnf(c565,plain,
double_divide(X2,X) = inverse(multiply(X,X2)),
inference(symmetry,[status(thm)],[c564]) ).
cnf(c566,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c476]) ).
cnf(c567,plain,
multiply(X,X2) = multiply(X,inverse(inverse(X2))),
inference(congruence,[status(thm)],[c566]) ).
cnf(c568,plain,
inverse(multiply(X,X2)) = inverse(multiply(X,inverse(inverse(X2)))),
inference(congruence,[status(thm)],[c567]) ).
cnf(c569,plain,
inverse(multiply(X,inverse(inverse(X2)))) = double_divide(X2,inverse(inverse(X))),
inference(substitution,[status(thm)],[c295]) ).
cnf(c570,plain,
double_divide(X2,inverse(inverse(X))) = multiply(inverse(X2),inverse(X)),
inference(substitution,[status(thm)],[c462]) ).
cnf(c571,plain,
inverse(multiply(X,inverse(inverse(X2)))) = multiply(inverse(X2),inverse(X)),
inference(transitivity,[status(thm)],[c569,c570]) ).
cnf(c572,plain,
inverse(multiply(X,X2)) = multiply(inverse(X2),inverse(X)),
inference(transitivity,[status(thm)],[c568,c571]) ).
cnf(c573,plain,
double_divide(X2,X) = multiply(inverse(X2),inverse(X)),
inference(transitivity,[status(thm)],[c565,c572]) ).
cnf(c574,plain,
multiply(inverse(X2),inverse(X)) = double_divide(X2,X),
inference(symmetry,[status(thm)],[c573]) ).
cnf(c575,plain,
multiply(multiply(inverse(X3),inverse(X2)),inverse(X)) = multiply(double_divide(X3,X2),inverse(X)),
inference(congruence,[status(thm)],[c574]) ).
cnf(c576,plain,
multiply(X3,multiply(multiply(inverse(X3),inverse(X2)),inverse(X))) = multiply(X3,multiply(double_divide(X3,X2),inverse(X))),
inference(congruence,[status(thm)],[c575]) ).
cnf(c577,plain,
inverse(double_divide(inverse(X),double_divide(X3,X2))) = multiply(double_divide(X3,X2),inverse(X)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c578,plain,
multiply(double_divide(X3,X2),inverse(X)) = inverse(double_divide(inverse(X),double_divide(X3,X2))),
inference(symmetry,[status(thm)],[c577]) ).
cnf(c579,plain,
multiply(X3,multiply(double_divide(X3,X2),inverse(X))) = multiply(X3,inverse(double_divide(inverse(X),double_divide(X3,X2)))),
inference(congruence,[status(thm)],[c578]) ).
cnf(c580,plain,
inverse(inverse(double_divide(identity,X))) = double_divide(identity,X),
inference(substitution,[status(thm)],[c476]) ).
cnf(c581,plain,
double_divide(identity,X) = inverse(inverse(double_divide(identity,X))),
inference(symmetry,[status(thm)],[c580]) ).
cnf(c582,plain,
multiply(identity,double_divide(identity,X)) = inverse(inverse(double_divide(identity,X))),
inference(substitution,[status(thm)],[c67]) ).
cnf(c583,plain,
inverse(inverse(double_divide(identity,X))) = multiply(identity,double_divide(identity,X)),
inference(symmetry,[status(thm)],[c582]) ).
cnf(c584,plain,
multiply(identity,double_divide(identity,X)) = inverse(X),
inference(substitution,[status(thm)],[c542]) ).
cnf(c585,plain,
inverse(inverse(double_divide(identity,X))) = inverse(X),
inference(transitivity,[status(thm)],[c583,c584]) ).
cnf(c586,plain,
double_divide(identity,X) = inverse(X),
inference(transitivity,[status(thm)],[c581,c585]) ).
cnf(c587,plain,
double_divide(identity,double_divide(inverse(X),double_divide(X3,X2))) = inverse(double_divide(inverse(X),double_divide(X3,X2))),
inference(substitution,[status(thm)],[c586]) ).
cnf(c588,plain,
inverse(double_divide(inverse(X),double_divide(X3,X2))) = double_divide(identity,double_divide(inverse(X),double_divide(X3,X2))),
inference(symmetry,[status(thm)],[c587]) ).
cnf(c589,plain,
multiply(X3,inverse(double_divide(inverse(X),double_divide(X3,X2)))) = multiply(X3,double_divide(identity,double_divide(inverse(X),double_divide(X3,X2)))),
inference(congruence,[status(thm)],[c588]) ).
cnf(c590,plain,
inverse(multiply(X2,double_divide(X2,X))) = double_divide(double_divide(X2,X),X2),
inference(substitution,[status(thm)],[c506]) ).
cnf(c591,plain,
double_divide(double_divide(X2,X),X2) = inverse(multiply(X2,double_divide(X2,X))),
inference(symmetry,[status(thm)],[c590]) ).
cnf(c592,plain,
inverse(multiply(X2,double_divide(X2,X))) = inverse(inverse(X)),
inference(congruence,[status(thm)],[c542]) ).
cnf(c593,plain,
inverse(multiply(X2,double_divide(X2,X))) = X,
inference(transitivity,[status(thm)],[c592,c476]) ).
cnf(c594,plain,
double_divide(double_divide(X2,X),X2) = X,
inference(transitivity,[status(thm)],[c591,c593]) ).
cnf(c595,plain,
double_divide(double_divide(X,multiply(X3,double_divide(identity,double_divide(inverse(X),double_divide(X3,X2))))),X) = multiply(X3,double_divide(identity,double_divide(inverse(X),double_divide(X3,X2)))),
inference(substitution,[status(thm)],[c594]) ).
cnf(c596,plain,
multiply(X3,double_divide(identity,double_divide(inverse(X),double_divide(X3,X2)))) = double_divide(double_divide(X,multiply(X3,double_divide(identity,double_divide(inverse(X),double_divide(X3,X2))))),X),
inference(symmetry,[status(thm)],[c595]) ).
cnf(c597,plain,
double_divide(X,multiply(X3,double_divide(identity,double_divide(inverse(X),double_divide(X3,X2))))) = X2,
inference(substitution,[status(thm)],[c40]) ).
cnf(c598,plain,
double_divide(double_divide(X,multiply(X3,double_divide(identity,double_divide(inverse(X),double_divide(X3,X2))))),X) = double_divide(X2,X),
inference(congruence,[status(thm)],[c597]) ).
cnf(c599,plain,
double_divide(double_divide(X,multiply(X3,double_divide(identity,double_divide(inverse(X),double_divide(X3,X2))))),X) = multiply(inverse(X2),inverse(X)),
inference(transitivity,[status(thm)],[c598,c573]) ).
cnf(c600,plain,
multiply(X3,double_divide(identity,double_divide(inverse(X),double_divide(X3,X2)))) = multiply(inverse(X2),inverse(X)),
inference(transitivity,[status(thm)],[c596,c599]) ).
cnf(c601,plain,
multiply(X3,inverse(double_divide(inverse(X),double_divide(X3,X2)))) = multiply(inverse(X2),inverse(X)),
inference(transitivity,[status(thm)],[c589,c600]) ).
cnf(c602,plain,
multiply(X3,multiply(double_divide(X3,X2),inverse(X))) = multiply(inverse(X2),inverse(X)),
inference(transitivity,[status(thm)],[c579,c601]) ).
cnf(c603,plain,
multiply(X3,multiply(multiply(inverse(X3),inverse(X2)),inverse(X))) = multiply(inverse(X2),inverse(X)),
inference(transitivity,[status(thm)],[c576,c602]) ).
cnf(c604,plain,
multiply(X,multiply(multiply(inverse(X),inverse(X2)),inverse(X3))) = multiply(inverse(X2),inverse(X3)),
inference(substitution,[status(thm)],[c603]) ).
cnf(c605,plain,
inverse(multiply(X,multiply(multiply(inverse(X),inverse(X2)),inverse(X3)))) = inverse(multiply(inverse(X2),inverse(X3))),
inference(congruence,[status(thm)],[c604]) ).
cnf(c606,plain,
inverse(multiply(inverse(X),inverse(X2))) = multiply(inverse(inverse(X2)),X),
inference(substitution,[status(thm)],[c453]) ).
cnf(c607,plain,
multiply(X2,inverse(inverse(X))) = multiply(X2,X),
inference(congruence,[status(thm)],[c476]) ).
cnf(c608,plain,
multiply(inverse(inverse(X2)),X) = multiply(X2,X),
inference(transitivity,[status(thm)],[c222,c607]) ).
cnf(c609,plain,
inverse(multiply(inverse(X),inverse(X2))) = multiply(X2,X),
inference(transitivity,[status(thm)],[c606,c608]) ).
cnf(c610,plain,
inverse(multiply(X,multiply(multiply(inverse(X),inverse(X2)),inverse(X3)))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c605,c609]) ).
cnf(c611,plain,
double_divide(multiply(multiply(inverse(X),inverse(X2)),inverse(X3)),inverse(inverse(X))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c563,c610]) ).
cnf(c612,plain,
multiply(inverse(multiply(multiply(inverse(X),inverse(X2)),inverse(X3))),inverse(X)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c557,c611]) ).
cnf(c613,plain,
multiply(double_divide(inverse(X3),multiply(inverse(X),inverse(X2))),inverse(inverse(inverse(X)))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c555,c612]) ).
cnf(c614,plain,
multiply(multiply(X3,inverse(multiply(inverse(X),inverse(X2)))),inverse(inverse(inverse(X)))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c553,c613]) ).
cnf(c615,plain,
multiply(multiply(X3,inverse(multiply(inverse(X),inverse(X2)))),inverse(X)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c493,c614]) ).
cnf(c616,plain,
multiply(multiply(X3,multiply(inverse(inverse(X2)),X)),inverse(X)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c487,c615]) ).
cnf(c617,plain,
multiply(multiply(X3,multiply(X2,inverse(inverse(X)))),inverse(X)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c483,c616]) ).
cnf(c618,plain,
multiply(multiply(X3,multiply(X2,X)),inverse(X)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c480,c617]) ).
cnf(c619,plain,
multiply(X3,X2) = multiply(multiply(X3,multiply(X2,X)),inverse(X)),
inference(symmetry,[status(thm)],[c618]) ).
cnf(c620,plain,
multiply(multiply(X3,X2),X) = multiply(multiply(multiply(X3,multiply(X2,X)),inverse(X)),X),
inference(congruence,[status(thm)],[c619]) ).
cnf(c621,plain,
multiply(multiply(multiply(X3,multiply(X2,X)),inverse(X)),X) = inverse(inverse(multiply(X3,multiply(X2,X)))),
inference(substitution,[status(thm)],[c215]) ).
cnf(c622,plain,
inverse(inverse(multiply(X3,multiply(X2,X)))) = multiply(X3,multiply(X2,X)),
inference(substitution,[status(thm)],[c169]) ).
cnf(c623,plain,
multiply(multiply(multiply(X3,multiply(X2,X)),inverse(X)),X) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c621,c622]) ).
cnf(c624,plain,
multiply(multiply(X3,X2),X) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c620,c623]) ).
cnf(c625,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(substitution,[status(thm)],[c624]) ).
cnf(c626,plain,
$false,
inference(resolution,[status(thm)],[c1,c625]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP489-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 10:06:40 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/0.52 Command-line arguments: --no-flatten-goal
% 0.55/0.52
% 0.55/0.52 % SZS status Unsatisfiable
% 0.55/0.52
% 0.55/0.56 % SZS output start CNFRefutation
% See solution above
% 3.02/0.84
% 3.02/0.84 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------