%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP579-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:11:17 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.52s
% Output : CNFRefutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 90
% Number of leaves : 5
% Syntax : Number of clauses : 468 ( 468 unt; 0 nHn; 50 RR)
% Number of literals : 468 ( 467 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 723 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(c2,axiom,
inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(c3,plain,
inverse(double_divide(X2,X)) = double_divide(double_divide(X2,X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
multiply(A2,B) = double_divide(double_divide(B,A2),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c5,plain,
multiply(X,X2) = double_divide(double_divide(X2,X),identity),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
double_divide(double_divide(X2,X),identity) = multiply(X,X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
inverse(double_divide(X2,X)) = multiply(X,X2),
inference(transitivity,[status(thm)],[c3,c6]) ).
cnf(c8,plain,
inverse(double_divide(X,identity)) = multiply(identity,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(identity,X) = inverse(double_divide(X,identity)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c11,plain,
double_divide(X,identity) = inverse(X),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
inverse(double_divide(X,identity)) = inverse(inverse(X)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(identity,X) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c9,c12]) ).
cnf(c14,plain,
multiply(identity,inverse(X)) = inverse(inverse(inverse(X))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
inverse(inverse(inverse(X))) = multiply(identity,inverse(X)),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
inverse(inverse(inverse(inverse(X)))) = inverse(multiply(identity,inverse(X))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
inverse(double_divide(X,inverse(X))) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c18,plain,
multiply(inverse(X),X) = inverse(double_divide(X,inverse(X))),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,axiom,
identity = double_divide(A2,inverse(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(c20,plain,
identity = double_divide(X,inverse(X)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
double_divide(X,inverse(X)) = identity,
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
inverse(double_divide(X,inverse(X))) = inverse(identity),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(inverse(X),X) = inverse(identity),
inference(transitivity,[status(thm)],[c18,c22]) ).
cnf(c24,plain,
multiply(inverse(identity),identity) = inverse(identity),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
inverse(identity) = multiply(inverse(identity),identity),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c27,plain,
double_divide(inverse(X),inverse(identity)) = double_divide(double_divide(X,identity),inverse(identity)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
identity = double_divide(identity,inverse(identity)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c29,plain,
double_divide(X,identity) = double_divide(X,double_divide(identity,inverse(identity))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
double_divide(double_divide(X,identity),inverse(identity)) = double_divide(double_divide(X,double_divide(identity,inverse(identity))),inverse(identity)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
identity = double_divide(double_divide(X,X2),inverse(double_divide(X,X2))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c32,plain,
double_divide(identity,inverse(X)) = double_divide(double_divide(double_divide(X,X2),inverse(double_divide(X,X2))),inverse(X)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
double_divide(X2,double_divide(identity,inverse(X))) = double_divide(X2,double_divide(double_divide(double_divide(X,X2),inverse(double_divide(X,X2))),inverse(X))),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
double_divide(double_divide(X2,double_divide(identity,inverse(X))),inverse(identity)) = double_divide(double_divide(X2,double_divide(double_divide(double_divide(X,X2),inverse(double_divide(X,X2))),inverse(X))),inverse(identity)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
inverse(identity) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c36,plain,
double_divide(double_divide(X2,double_divide(double_divide(double_divide(X,X2),X3),inverse(X))),inverse(identity)) = double_divide(double_divide(X2,double_divide(double_divide(double_divide(X,X2),X3),inverse(X))),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c38,plain,
double_divide(double_divide(double_divide(X2,X3),X),inverse(X2)) = double_divide(double_divide(double_divide(X2,X3),X),double_divide(X2,identity)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
double_divide(X3,double_divide(double_divide(double_divide(X2,X3),X),inverse(X2))) = double_divide(X3,double_divide(double_divide(double_divide(X2,X3),X),double_divide(X2,identity))),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
double_divide(double_divide(X3,double_divide(double_divide(double_divide(X2,X3),X),inverse(X2))),double_divide(identity,identity)) = double_divide(double_divide(X3,double_divide(double_divide(double_divide(X2,X3),X),double_divide(X2,identity))),double_divide(identity,identity)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,axiom,
double_divide(double_divide(A2,double_divide(double_divide(double_divide(B2,A2),C),double_divide(B2,identity))),double_divide(identity,identity)) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c42,plain,
double_divide(double_divide(X3,double_divide(double_divide(double_divide(X2,X3),X),double_divide(X2,identity))),double_divide(identity,identity)) = X,
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
double_divide(double_divide(X3,double_divide(double_divide(double_divide(X2,X3),X),inverse(X2))),double_divide(identity,identity)) = X,
inference(transitivity,[status(thm)],[c40,c42]) ).
cnf(c44,plain,
double_divide(double_divide(X3,double_divide(double_divide(double_divide(X2,X3),X),inverse(X2))),inverse(identity)) = X,
inference(transitivity,[status(thm)],[c36,c43]) ).
cnf(c45,plain,
double_divide(double_divide(X2,double_divide(double_divide(double_divide(X,X2),inverse(double_divide(X,X2))),inverse(X))),inverse(identity)) = inverse(double_divide(X,X2)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c47,plain,
double_divide(double_divide(X2,double_divide(double_divide(double_divide(X,X2),inverse(double_divide(X,X2))),inverse(X))),inverse(identity)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c45,c46]) ).
cnf(c48,plain,
double_divide(double_divide(X2,double_divide(identity,inverse(X))),inverse(identity)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c34,c47]) ).
cnf(c49,plain,
double_divide(double_divide(X,double_divide(identity,inverse(identity))),inverse(identity)) = multiply(X,identity),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
double_divide(double_divide(X,identity),inverse(identity)) = multiply(X,identity),
inference(transitivity,[status(thm)],[c30,c49]) ).
cnf(c51,plain,
double_divide(inverse(X),inverse(identity)) = multiply(X,identity),
inference(transitivity,[status(thm)],[c27,c50]) ).
cnf(c52,plain,
double_divide(inverse(inverse(identity)),inverse(identity)) = multiply(inverse(identity),identity),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
multiply(inverse(identity),identity) = double_divide(inverse(inverse(identity)),inverse(identity)),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
inverse(inverse(identity)) = double_divide(inverse(identity),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c55,plain,
double_divide(inverse(inverse(identity)),inverse(identity)) = double_divide(double_divide(inverse(identity),identity),inverse(identity)),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
identity = double_divide(inverse(inverse(identity)),inverse(inverse(inverse(identity)))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c57,plain,
double_divide(inverse(identity),identity) = double_divide(inverse(identity),double_divide(inverse(inverse(identity)),inverse(inverse(inverse(identity))))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
double_divide(double_divide(inverse(identity),identity),inverse(identity)) = double_divide(double_divide(inverse(identity),double_divide(inverse(inverse(identity)),inverse(inverse(inverse(identity))))),inverse(identity)),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
multiply(X,identity) = double_divide(inverse(X),inverse(identity)),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c60,plain,
inverse(multiply(X,identity)) = inverse(double_divide(inverse(X),inverse(identity))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
inverse(double_divide(inverse(X),inverse(identity))) = multiply(inverse(identity),inverse(X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c62,plain,
inverse(multiply(X,identity)) = multiply(inverse(identity),inverse(X)),
inference(transitivity,[status(thm)],[c60,c61]) ).
cnf(c63,plain,
inverse(multiply(inverse(identity),identity)) = multiply(inverse(identity),inverse(inverse(identity))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
multiply(inverse(identity),inverse(inverse(identity))) = inverse(multiply(inverse(identity),identity)),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
multiply(inverse(identity),identity) = inverse(identity),
inference(substitution,[status(thm)],[c23]) ).
cnf(c66,plain,
inverse(multiply(inverse(identity),identity)) = inverse(inverse(identity)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
multiply(inverse(identity),inverse(inverse(identity))) = inverse(inverse(identity)),
inference(transitivity,[status(thm)],[c64,c66]) ).
cnf(c68,plain,
inverse(inverse(identity)) = multiply(inverse(identity),inverse(inverse(identity))),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
double_divide(inverse(inverse(identity)),inverse(inverse(inverse(identity)))) = double_divide(multiply(inverse(identity),inverse(inverse(identity))),inverse(inverse(inverse(identity)))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
double_divide(inverse(identity),double_divide(inverse(inverse(identity)),inverse(inverse(inverse(identity))))) = double_divide(inverse(identity),double_divide(multiply(inverse(identity),inverse(inverse(identity))),inverse(inverse(inverse(identity))))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
double_divide(double_divide(inverse(identity),double_divide(inverse(inverse(identity)),inverse(inverse(inverse(identity))))),inverse(identity)) = double_divide(double_divide(inverse(identity),double_divide(multiply(inverse(identity),inverse(inverse(identity))),inverse(inverse(inverse(identity))))),inverse(identity)),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c73,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
double_divide(multiply(X2,X),inverse(X)) = double_divide(inverse(double_divide(X,X2)),inverse(X)),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
double_divide(X2,double_divide(multiply(X2,X),inverse(X))) = double_divide(X2,double_divide(inverse(double_divide(X,X2)),inverse(X))),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
double_divide(double_divide(X2,double_divide(multiply(X2,X),inverse(X))),inverse(identity)) = double_divide(double_divide(X2,double_divide(inverse(double_divide(X,X2)),inverse(X))),inverse(identity)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
inverse(double_divide(X,X2)) = double_divide(double_divide(X,X2),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c78,plain,
double_divide(inverse(double_divide(X,X2)),inverse(X)) = double_divide(double_divide(double_divide(X,X2),identity),inverse(X)),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
double_divide(X2,double_divide(inverse(double_divide(X,X2)),inverse(X))) = double_divide(X2,double_divide(double_divide(double_divide(X,X2),identity),inverse(X))),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
double_divide(double_divide(X2,double_divide(inverse(double_divide(X,X2)),inverse(X))),inverse(identity)) = double_divide(double_divide(X2,double_divide(double_divide(double_divide(X,X2),identity),inverse(X))),inverse(identity)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
double_divide(double_divide(X2,double_divide(double_divide(double_divide(X,X2),identity),inverse(X))),inverse(identity)) = identity,
inference(substitution,[status(thm)],[c44]) ).
cnf(c82,plain,
double_divide(double_divide(X2,double_divide(inverse(double_divide(X,X2)),inverse(X))),inverse(identity)) = identity,
inference(transitivity,[status(thm)],[c80,c81]) ).
cnf(c83,plain,
double_divide(double_divide(X2,double_divide(multiply(X2,X),inverse(X))),inverse(identity)) = identity,
inference(transitivity,[status(thm)],[c76,c82]) ).
cnf(c84,plain,
double_divide(double_divide(inverse(identity),double_divide(multiply(inverse(identity),inverse(inverse(identity))),inverse(inverse(inverse(identity))))),inverse(identity)) = identity,
inference(substitution,[status(thm)],[c83]) ).
cnf(c85,plain,
double_divide(double_divide(inverse(identity),double_divide(inverse(inverse(identity)),inverse(inverse(inverse(identity))))),inverse(identity)) = identity,
inference(transitivity,[status(thm)],[c71,c84]) ).
cnf(c86,plain,
double_divide(double_divide(inverse(identity),identity),inverse(identity)) = identity,
inference(transitivity,[status(thm)],[c58,c85]) ).
cnf(c87,plain,
double_divide(inverse(inverse(identity)),inverse(identity)) = identity,
inference(transitivity,[status(thm)],[c55,c86]) ).
cnf(c88,plain,
multiply(inverse(identity),identity) = identity,
inference(transitivity,[status(thm)],[c53,c87]) ).
cnf(c89,plain,
inverse(identity) = identity,
inference(transitivity,[status(thm)],[c25,c88]) ).
cnf(c90,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
multiply(identity,inverse(X)) = multiply(inverse(identity),inverse(X)),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
inverse(multiply(identity,inverse(X))) = inverse(multiply(inverse(identity),inverse(X))),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
multiply(inverse(identity),inverse(X)) = inverse(multiply(X,identity)),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c94,plain,
inverse(multiply(inverse(identity),inverse(X))) = inverse(inverse(multiply(X,identity))),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
inverse(double_divide(identity,X)) = multiply(X,identity),
inference(substitution,[status(thm)],[c7]) ).
cnf(c96,plain,
multiply(X,identity) = inverse(double_divide(identity,X)),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
inverse(multiply(X,identity)) = inverse(inverse(double_divide(identity,X))),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
inverse(inverse(multiply(X,identity))) = inverse(inverse(inverse(double_divide(identity,X)))),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
multiply(identity,inverse(double_divide(identity,X))) = inverse(inverse(inverse(double_divide(identity,X)))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c100,plain,
inverse(inverse(inverse(double_divide(identity,X)))) = multiply(identity,inverse(double_divide(identity,X))),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c102,plain,
multiply(identity,inverse(double_divide(identity,X))) = multiply(inverse(identity),inverse(double_divide(identity,X))),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
inverse(multiply(double_divide(identity,X),identity)) = multiply(inverse(identity),inverse(double_divide(identity,X))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c104,plain,
multiply(inverse(identity),inverse(double_divide(identity,X))) = inverse(multiply(double_divide(identity,X),identity)),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
inverse(double_divide(identity,double_divide(identity,X))) = multiply(double_divide(identity,X),identity),
inference(substitution,[status(thm)],[c7]) ).
cnf(c106,plain,
multiply(double_divide(identity,X),identity) = inverse(double_divide(identity,double_divide(identity,X))),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
inverse(multiply(double_divide(identity,X),identity)) = inverse(inverse(double_divide(identity,double_divide(identity,X)))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
double_divide(double_divide(X,double_divide(identity,inverse(identity))),inverse(identity)) = multiply(X,identity),
inference(substitution,[status(thm)],[c48]) ).
cnf(c109,plain,
multiply(X,identity) = double_divide(double_divide(X,double_divide(identity,inverse(identity))),inverse(identity)),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
double_divide(identity,inverse(identity)) = double_divide(identity,identity),
inference(congruence,[status(thm)],[c89]) ).
cnf(c111,plain,
double_divide(X,double_divide(identity,inverse(identity))) = double_divide(X,double_divide(identity,identity)),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
double_divide(double_divide(X,double_divide(identity,inverse(identity))),inverse(identity)) = double_divide(double_divide(X,double_divide(identity,identity)),inverse(identity)),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
inverse(identity) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c114,plain,
double_divide(identity,identity) = inverse(identity),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
double_divide(X,double_divide(identity,identity)) = double_divide(X,inverse(identity)),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
double_divide(double_divide(X,double_divide(identity,identity)),inverse(identity)) = double_divide(double_divide(X,inverse(identity)),inverse(identity)),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
double_divide(X,inverse(identity)) = double_divide(X,identity),
inference(congruence,[status(thm)],[c89]) ).
cnf(c118,plain,
double_divide(double_divide(X,inverse(identity)),inverse(identity)) = double_divide(double_divide(X,identity),inverse(identity)),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
double_divide(double_divide(X,identity),inverse(identity)) = double_divide(double_divide(X,identity),identity),
inference(congruence,[status(thm)],[c89]) ).
cnf(c120,plain,
inverse(double_divide(X,identity)) = double_divide(double_divide(X,identity),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c121,plain,
double_divide(double_divide(X,identity),identity) = inverse(double_divide(X,identity)),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
inverse(double_divide(X,identity)) = multiply(identity,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c123,plain,
inverse(double_divide(X,identity)) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c122,c13]) ).
cnf(c124,plain,
double_divide(double_divide(X,identity),identity) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c121,c123]) ).
cnf(c125,plain,
double_divide(double_divide(X,identity),inverse(identity)) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c119,c124]) ).
cnf(c126,plain,
double_divide(double_divide(X,inverse(identity)),inverse(identity)) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c118,c125]) ).
cnf(c127,plain,
double_divide(double_divide(X,double_divide(identity,identity)),inverse(identity)) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c116,c126]) ).
cnf(c128,plain,
double_divide(double_divide(X,double_divide(identity,inverse(identity))),inverse(identity)) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c112,c127]) ).
cnf(c129,plain,
multiply(X,identity) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c109,c128]) ).
cnf(c130,plain,
multiply(double_divide(identity,double_divide(identity,X)),identity) = inverse(inverse(double_divide(identity,double_divide(identity,X)))),
inference(substitution,[status(thm)],[c129]) ).
cnf(c131,plain,
inverse(inverse(double_divide(identity,double_divide(identity,X)))) = multiply(double_divide(identity,double_divide(identity,X)),identity),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c133,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
double_divide(multiply(X2,X),inverse(identity)) = double_divide(inverse(double_divide(X,X2)),inverse(identity)),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
double_divide(inverse(double_divide(X,X2)),inverse(identity)) = multiply(double_divide(X,X2),identity),
inference(substitution,[status(thm)],[c51]) ).
cnf(c136,plain,
double_divide(multiply(X2,X),inverse(identity)) = multiply(double_divide(X,X2),identity),
inference(transitivity,[status(thm)],[c134,c135]) ).
cnf(c137,plain,
double_divide(multiply(double_divide(identity,X),identity),inverse(identity)) = multiply(double_divide(identity,double_divide(identity,X)),identity),
inference(substitution,[status(thm)],[c136]) ).
cnf(c138,plain,
multiply(double_divide(identity,double_divide(identity,X)),identity) = double_divide(multiply(double_divide(identity,X),identity),inverse(identity)),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
double_divide(double_divide(X2,double_divide(double_divide(double_divide(identity,X2),double_divide(multiply(double_divide(identity,X2),X),inverse(X))),inverse(identity))),inverse(identity)) = double_divide(multiply(double_divide(identity,X2),X),inverse(X)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c140,plain,
double_divide(multiply(double_divide(identity,X2),X),inverse(X)) = double_divide(double_divide(X2,double_divide(double_divide(double_divide(identity,X2),double_divide(multiply(double_divide(identity,X2),X),inverse(X))),inverse(identity))),inverse(identity)),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
double_divide(double_divide(double_divide(identity,X2),double_divide(multiply(double_divide(identity,X2),X),inverse(X))),inverse(identity)) = identity,
inference(substitution,[status(thm)],[c83]) ).
cnf(c142,plain,
double_divide(X2,double_divide(double_divide(double_divide(identity,X2),double_divide(multiply(double_divide(identity,X2),X),inverse(X))),inverse(identity))) = double_divide(X2,identity),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
double_divide(double_divide(X2,double_divide(double_divide(double_divide(identity,X2),double_divide(multiply(double_divide(identity,X2),X),inverse(X))),inverse(identity))),inverse(identity)) = double_divide(double_divide(X2,identity),inverse(identity)),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c145,plain,
double_divide(X,identity) = inverse(X),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c146,plain,
double_divide(double_divide(X,identity),inverse(identity)) = double_divide(inverse(X),inverse(identity)),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
double_divide(inverse(X),inverse(identity)) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c51,c129]) ).
cnf(c148,plain,
double_divide(double_divide(X,identity),inverse(identity)) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c146,c147]) ).
cnf(c149,plain,
double_divide(double_divide(X2,double_divide(double_divide(double_divide(identity,X2),double_divide(multiply(double_divide(identity,X2),X),inverse(X))),inverse(identity))),inverse(identity)) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c143,c148]) ).
cnf(c150,plain,
double_divide(multiply(double_divide(identity,X2),X),inverse(X)) = inverse(inverse(X2)),
inference(transitivity,[status(thm)],[c140,c149]) ).
cnf(c151,plain,
double_divide(multiply(double_divide(identity,X),identity),inverse(identity)) = inverse(inverse(X)),
inference(substitution,[status(thm)],[c150]) ).
cnf(c152,plain,
multiply(double_divide(identity,double_divide(identity,X)),identity) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c138,c151]) ).
cnf(c153,plain,
inverse(inverse(double_divide(identity,double_divide(identity,X)))) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c131,c152]) ).
cnf(c154,plain,
inverse(multiply(double_divide(identity,X),identity)) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c107,c153]) ).
cnf(c155,plain,
multiply(inverse(identity),inverse(double_divide(identity,X))) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c104,c154]) ).
cnf(c156,plain,
multiply(identity,inverse(double_divide(identity,X))) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c102,c155]) ).
cnf(c157,plain,
inverse(inverse(inverse(double_divide(identity,X)))) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c100,c156]) ).
cnf(c158,plain,
inverse(inverse(multiply(X,identity))) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c98,c157]) ).
cnf(c159,plain,
inverse(multiply(inverse(identity),inverse(X))) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c94,c158]) ).
cnf(c160,plain,
inverse(multiply(identity,inverse(X))) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c92,c159]) ).
cnf(c161,plain,
inverse(inverse(inverse(inverse(X)))) = inverse(inverse(X)),
inference(transitivity,[status(thm)],[c16,c160]) ).
cnf(c162,plain,
inverse(inverse(X)) = inverse(inverse(inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c161]) ).
cnf(c163,plain,
multiply(identity,inverse(X)) = inverse(inverse(inverse(X))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c164,plain,
inverse(inverse(inverse(X))) = multiply(identity,inverse(X)),
inference(symmetry,[status(thm)],[c163]) ).
cnf(c165,plain,
inverse(inverse(inverse(inverse(X)))) = inverse(multiply(identity,inverse(X))),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c167,plain,
multiply(identity,inverse(X)) = multiply(inverse(identity),inverse(X)),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
inverse(multiply(identity,inverse(X))) = inverse(multiply(inverse(identity),inverse(X))),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
multiply(inverse(identity),inverse(X)) = inverse(multiply(X,identity)),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c170,plain,
inverse(multiply(inverse(identity),inverse(X))) = inverse(inverse(multiply(X,identity))),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c172,plain,
multiply(X,identity) = multiply(X,inverse(identity)),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
inverse(multiply(X,identity)) = inverse(multiply(X,inverse(identity))),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
inverse(inverse(multiply(X,identity))) = inverse(inverse(multiply(X,inverse(identity)))),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
multiply(multiply(X,inverse(identity)),identity) = inverse(inverse(multiply(X,inverse(identity)))),
inference(substitution,[status(thm)],[c129]) ).
cnf(c176,plain,
inverse(inverse(multiply(X,inverse(identity)))) = multiply(multiply(X,inverse(identity)),identity),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
inverse(identity) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c178,plain,
multiply(X,inverse(identity)) = multiply(X,double_divide(identity,identity)),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
multiply(multiply(X,inverse(identity)),identity) = multiply(multiply(X,double_divide(identity,identity)),identity),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
inverse(double_divide(X,multiply(X2,double_divide(identity,X)))) = multiply(multiply(X2,double_divide(identity,X)),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c181,plain,
multiply(multiply(X2,double_divide(identity,X)),X) = inverse(double_divide(X,multiply(X2,double_divide(identity,X)))),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c182,plain,
inverse(double_divide(X,multiply(X2,double_divide(identity,X)))) = double_divide(double_divide(X,multiply(X2,double_divide(identity,X))),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c183,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c184,plain,
double_divide(double_divide(X,multiply(X2,double_divide(identity,X))),identity) = double_divide(double_divide(X,multiply(X2,double_divide(identity,X))),inverse(identity)),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
inverse(double_divide(double_divide(identity,X),X2)) = multiply(X2,double_divide(identity,X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c186,plain,
multiply(X2,double_divide(identity,X)) = inverse(double_divide(double_divide(identity,X),X2)),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,plain,
double_divide(X,multiply(X2,double_divide(identity,X))) = double_divide(X,inverse(double_divide(double_divide(identity,X),X2))),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
double_divide(double_divide(X,multiply(X2,double_divide(identity,X))),inverse(identity)) = double_divide(double_divide(X,inverse(double_divide(double_divide(identity,X),X2))),inverse(identity)),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
inverse(double_divide(double_divide(identity,X),X2)) = double_divide(double_divide(double_divide(identity,X),X2),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c190,plain,
double_divide(X,inverse(double_divide(double_divide(identity,X),X2))) = double_divide(X,double_divide(double_divide(double_divide(identity,X),X2),identity)),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
double_divide(double_divide(X,inverse(double_divide(double_divide(identity,X),X2))),inverse(identity)) = double_divide(double_divide(X,double_divide(double_divide(double_divide(identity,X),X2),identity)),inverse(identity)),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c193,plain,
double_divide(double_divide(double_divide(identity,X),X2),identity) = double_divide(double_divide(double_divide(identity,X),X2),inverse(identity)),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
double_divide(X,double_divide(double_divide(double_divide(identity,X),X2),identity)) = double_divide(X,double_divide(double_divide(double_divide(identity,X),X2),inverse(identity))),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
double_divide(double_divide(X,double_divide(double_divide(double_divide(identity,X),X2),identity)),inverse(identity)) = double_divide(double_divide(X,double_divide(double_divide(double_divide(identity,X),X2),inverse(identity))),inverse(identity)),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
double_divide(double_divide(X,double_divide(double_divide(double_divide(identity,X),X2),inverse(identity))),inverse(identity)) = X2,
inference(substitution,[status(thm)],[c44]) ).
cnf(c197,plain,
double_divide(double_divide(X,double_divide(double_divide(double_divide(identity,X),X2),identity)),inverse(identity)) = X2,
inference(transitivity,[status(thm)],[c195,c196]) ).
cnf(c198,plain,
double_divide(double_divide(X,inverse(double_divide(double_divide(identity,X),X2))),inverse(identity)) = X2,
inference(transitivity,[status(thm)],[c191,c197]) ).
cnf(c199,plain,
double_divide(double_divide(X,multiply(X2,double_divide(identity,X))),inverse(identity)) = X2,
inference(transitivity,[status(thm)],[c188,c198]) ).
cnf(c200,plain,
double_divide(double_divide(X,multiply(X2,double_divide(identity,X))),identity) = X2,
inference(transitivity,[status(thm)],[c184,c199]) ).
cnf(c201,plain,
inverse(double_divide(X,multiply(X2,double_divide(identity,X)))) = X2,
inference(transitivity,[status(thm)],[c182,c200]) ).
cnf(c202,plain,
multiply(multiply(X2,double_divide(identity,X)),X) = X2,
inference(transitivity,[status(thm)],[c181,c201]) ).
cnf(c203,plain,
multiply(multiply(X,double_divide(identity,identity)),identity) = X,
inference(substitution,[status(thm)],[c202]) ).
cnf(c204,plain,
multiply(multiply(X,inverse(identity)),identity) = X,
inference(transitivity,[status(thm)],[c179,c203]) ).
cnf(c205,plain,
inverse(inverse(multiply(X,inverse(identity)))) = X,
inference(transitivity,[status(thm)],[c176,c204]) ).
cnf(c206,plain,
inverse(inverse(multiply(X,identity))) = X,
inference(transitivity,[status(thm)],[c174,c205]) ).
cnf(c207,plain,
inverse(multiply(inverse(identity),inverse(X))) = X,
inference(transitivity,[status(thm)],[c170,c206]) ).
cnf(c208,plain,
inverse(multiply(identity,inverse(X))) = X,
inference(transitivity,[status(thm)],[c168,c207]) ).
cnf(c209,plain,
inverse(inverse(inverse(inverse(X)))) = X,
inference(transitivity,[status(thm)],[c165,c208]) ).
cnf(c210,plain,
inverse(inverse(X)) = X,
inference(transitivity,[status(thm)],[c162,c209]) ).
cnf(c211,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c212,plain,
multiply(X,X2) = multiply(X,inverse(inverse(X2))),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
inverse(double_divide(X2,inverse(inverse(inverse(X))))) = multiply(inverse(inverse(inverse(X))),X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c214,plain,
multiply(inverse(inverse(inverse(X))),X2) = inverse(double_divide(X2,inverse(inverse(inverse(X))))),
inference(symmetry,[status(thm)],[c213]) ).
cnf(c215,plain,
inverse(double_divide(X2,inverse(inverse(inverse(X))))) = double_divide(double_divide(X2,inverse(inverse(inverse(X)))),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c216,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c217,plain,
double_divide(double_divide(X2,inverse(inverse(inverse(X)))),identity) = double_divide(double_divide(X2,inverse(inverse(inverse(X)))),inverse(identity)),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c219,plain,
double_divide(identity,inverse(X)) = double_divide(inverse(identity),inverse(X)),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
multiply(double_divide(identity,inverse(X)),inverse(X)) = multiply(double_divide(inverse(identity),inverse(X)),inverse(X)),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
inverse(identity) = multiply(inverse(X),X),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c222,plain,
double_divide(inverse(identity),inverse(X)) = double_divide(multiply(inverse(X),X),inverse(X)),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
multiply(double_divide(inverse(identity),inverse(X)),inverse(X)) = multiply(double_divide(multiply(inverse(X),X),inverse(X)),inverse(X)),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
double_divide(double_divide(double_divide(multiply(X2,X),inverse(X)),double_divide(identity,inverse(X2))),inverse(identity)) = multiply(double_divide(multiply(X2,X),inverse(X)),X2),
inference(substitution,[status(thm)],[c48]) ).
cnf(c225,plain,
multiply(double_divide(multiply(X2,X),inverse(X)),X2) = double_divide(double_divide(double_divide(multiply(X2,X),inverse(X)),double_divide(identity,inverse(X2))),inverse(identity)),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c226,plain,
identity = double_divide(double_divide(X2,double_divide(multiply(X2,X),inverse(X))),inverse(identity)),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c227,plain,
double_divide(identity,inverse(X2)) = double_divide(double_divide(double_divide(X2,double_divide(multiply(X2,X),inverse(X))),inverse(identity)),inverse(X2)),
inference(congruence,[status(thm)],[c226]) ).
cnf(c228,plain,
double_divide(double_divide(multiply(X2,X),inverse(X)),double_divide(identity,inverse(X2))) = double_divide(double_divide(multiply(X2,X),inverse(X)),double_divide(double_divide(double_divide(X2,double_divide(multiply(X2,X),inverse(X))),inverse(identity)),inverse(X2))),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
double_divide(double_divide(double_divide(multiply(X2,X),inverse(X)),double_divide(identity,inverse(X2))),inverse(identity)) = double_divide(double_divide(double_divide(multiply(X2,X),inverse(X)),double_divide(double_divide(double_divide(X2,double_divide(multiply(X2,X),inverse(X))),inverse(identity)),inverse(X2))),inverse(identity)),
inference(congruence,[status(thm)],[c228]) ).
cnf(c230,plain,
double_divide(double_divide(double_divide(multiply(X2,X),inverse(X)),double_divide(double_divide(double_divide(X2,double_divide(multiply(X2,X),inverse(X))),inverse(identity)),inverse(X2))),inverse(identity)) = inverse(identity),
inference(substitution,[status(thm)],[c44]) ).
cnf(c231,plain,
double_divide(double_divide(double_divide(multiply(X2,X),inverse(X)),double_divide(double_divide(double_divide(X2,double_divide(multiply(X2,X),inverse(X))),inverse(identity)),inverse(X2))),inverse(identity)) = identity,
inference(transitivity,[status(thm)],[c230,c89]) ).
cnf(c232,plain,
double_divide(double_divide(double_divide(multiply(X2,X),inverse(X)),double_divide(identity,inverse(X2))),inverse(identity)) = identity,
inference(transitivity,[status(thm)],[c229,c231]) ).
cnf(c233,plain,
multiply(double_divide(multiply(X2,X),inverse(X)),X2) = identity,
inference(transitivity,[status(thm)],[c225,c232]) ).
cnf(c234,plain,
multiply(double_divide(multiply(inverse(X),X),inverse(X)),inverse(X)) = identity,
inference(substitution,[status(thm)],[c233]) ).
cnf(c235,plain,
multiply(double_divide(inverse(identity),inverse(X)),inverse(X)) = identity,
inference(transitivity,[status(thm)],[c223,c234]) ).
cnf(c236,plain,
multiply(double_divide(identity,inverse(X)),inverse(X)) = identity,
inference(transitivity,[status(thm)],[c220,c235]) ).
cnf(c237,plain,
identity = multiply(double_divide(identity,inverse(X)),inverse(X)),
inference(symmetry,[status(thm)],[c236]) ).
cnf(c238,plain,
double_divide(identity,inverse(inverse(X))) = double_divide(multiply(double_divide(identity,inverse(X)),inverse(X)),inverse(inverse(X))),
inference(congruence,[status(thm)],[c237]) ).
cnf(c239,plain,
double_divide(multiply(double_divide(identity,inverse(X)),inverse(X)),inverse(inverse(X))) = inverse(inverse(inverse(X))),
inference(substitution,[status(thm)],[c150]) ).
cnf(c240,plain,
double_divide(identity,inverse(inverse(X))) = inverse(inverse(inverse(X))),
inference(transitivity,[status(thm)],[c238,c239]) ).
cnf(c241,plain,
inverse(inverse(inverse(X))) = double_divide(identity,inverse(inverse(X))),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c242,plain,
double_divide(X2,inverse(inverse(inverse(X)))) = double_divide(X2,double_divide(identity,inverse(inverse(X)))),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
double_divide(double_divide(X2,inverse(inverse(inverse(X)))),inverse(identity)) = double_divide(double_divide(X2,double_divide(identity,inverse(inverse(X)))),inverse(identity)),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
double_divide(double_divide(X2,double_divide(identity,inverse(inverse(X)))),inverse(identity)) = multiply(X2,inverse(X)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c245,plain,
double_divide(double_divide(X2,inverse(inverse(inverse(X)))),inverse(identity)) = multiply(X2,inverse(X)),
inference(transitivity,[status(thm)],[c243,c244]) ).
cnf(c246,plain,
double_divide(double_divide(X2,inverse(inverse(inverse(X)))),identity) = multiply(X2,inverse(X)),
inference(transitivity,[status(thm)],[c217,c245]) ).
cnf(c247,plain,
inverse(double_divide(X2,inverse(inverse(inverse(X))))) = multiply(X2,inverse(X)),
inference(transitivity,[status(thm)],[c215,c246]) ).
cnf(c248,plain,
multiply(inverse(inverse(inverse(X))),X2) = multiply(X2,inverse(X)),
inference(transitivity,[status(thm)],[c214,c247]) ).
cnf(c249,plain,
multiply(inverse(inverse(inverse(inverse(X2)))),X) = multiply(X,inverse(inverse(X2))),
inference(substitution,[status(thm)],[c248]) ).
cnf(c250,plain,
multiply(X,inverse(inverse(X2))) = multiply(inverse(inverse(inverse(inverse(X2)))),X),
inference(symmetry,[status(thm)],[c249]) ).
cnf(c251,plain,
multiply(inverse(inverse(inverse(inverse(X2)))),X) = multiply(inverse(inverse(X2)),X),
inference(congruence,[status(thm)],[c161]) ).
cnf(c252,plain,
multiply(inverse(inverse(X2)),X) = multiply(X2,X),
inference(congruence,[status(thm)],[c210]) ).
cnf(c253,plain,
multiply(inverse(inverse(inverse(inverse(X2)))),X) = multiply(X2,X),
inference(transitivity,[status(thm)],[c251,c252]) ).
cnf(c254,plain,
multiply(X,inverse(inverse(X2))) = multiply(X2,X),
inference(transitivity,[status(thm)],[c250,c253]) ).
cnf(c255,plain,
multiply(X,X2) = multiply(X2,X),
inference(transitivity,[status(thm)],[c212,c254]) ).
cnf(c256,plain,
multiply(c3,multiply(a3,b3)) = multiply(multiply(a3,b3),c3),
inference(substitution,[status(thm)],[c255]) ).
cnf(c257,plain,
multiply(multiply(a3,b3),c3) = multiply(c3,multiply(a3,b3)),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c258,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c259,plain,
multiply(X,multiply(X3,X2)) = multiply(inverse(inverse(X)),multiply(X3,X2)),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
inverse(inverse(X)) = inverse(inverse(inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c161]) ).
cnf(c261,plain,
multiply(inverse(inverse(X)),multiply(X3,X2)) = multiply(inverse(inverse(inverse(inverse(X)))),multiply(X3,X2)),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
multiply(X2,X) = multiply(X,X2),
inference(substitution,[status(thm)],[c255]) ).
cnf(c263,plain,
multiply(inverse(X3),multiply(X2,X)) = multiply(inverse(X3),multiply(X,X2)),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
inverse(inverse(inverse(X))) = inverse(X),
inference(substitution,[status(thm)],[c210]) ).
cnf(c265,plain,
inverse(X) = inverse(inverse(inverse(X))),
inference(symmetry,[status(thm)],[c264]) ).
cnf(c266,plain,
multiply(inverse(X3),multiply(X,X2)) = multiply(inverse(inverse(inverse(X3))),multiply(X,X2)),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,plain,
multiply(inverse(inverse(inverse(X3))),multiply(X,X2)) = multiply(multiply(X,X2),inverse(X3)),
inference(substitution,[status(thm)],[c248]) ).
cnf(c268,plain,
inverse(multiply(X2,X)) = double_divide(multiply(X2,X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c269,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c270,plain,
double_divide(multiply(X2,X),identity) = double_divide(multiply(X2,X),inverse(identity)),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
multiply(X2,X) = multiply(X,X2),
inference(substitution,[status(thm)],[c255]) ).
cnf(c272,plain,
double_divide(multiply(X2,X),inverse(identity)) = double_divide(multiply(X,X2),inverse(identity)),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
double_divide(multiply(X,X2),inverse(identity)) = multiply(double_divide(X2,X),identity),
inference(substitution,[status(thm)],[c136]) ).
cnf(c274,plain,
multiply(double_divide(X2,X),identity) = inverse(inverse(double_divide(X2,X))),
inference(substitution,[status(thm)],[c129]) ).
cnf(c275,plain,
inverse(inverse(double_divide(X2,X))) = double_divide(X2,X),
inference(substitution,[status(thm)],[c210]) ).
cnf(c276,plain,
multiply(double_divide(X2,X),identity) = double_divide(X2,X),
inference(transitivity,[status(thm)],[c274,c275]) ).
cnf(c277,plain,
double_divide(multiply(X,X2),inverse(identity)) = double_divide(X2,X),
inference(transitivity,[status(thm)],[c273,c276]) ).
cnf(c278,plain,
double_divide(multiply(X2,X),inverse(identity)) = double_divide(X2,X),
inference(transitivity,[status(thm)],[c272,c277]) ).
cnf(c279,plain,
double_divide(multiply(X2,X),identity) = double_divide(X2,X),
inference(transitivity,[status(thm)],[c270,c278]) ).
cnf(c280,plain,
inverse(multiply(X2,X)) = double_divide(X2,X),
inference(transitivity,[status(thm)],[c268,c279]) ).
cnf(c281,plain,
inverse(multiply(X,X2)) = double_divide(X,X2),
inference(substitution,[status(thm)],[c280]) ).
cnf(c282,plain,
double_divide(X,X2) = inverse(multiply(X,X2)),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c283,plain,
multiply(X,X2) = inverse(double_divide(X2,X)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c284,plain,
inverse(multiply(X,X2)) = inverse(inverse(double_divide(X2,X))),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
inverse(inverse(double_divide(X2,X))) = double_divide(X2,X),
inference(substitution,[status(thm)],[c210]) ).
cnf(c286,plain,
inverse(multiply(X,X2)) = double_divide(X2,X),
inference(transitivity,[status(thm)],[c284,c285]) ).
cnf(c287,plain,
double_divide(X,X2) = double_divide(X2,X),
inference(transitivity,[status(thm)],[c282,c286]) ).
cnf(c288,plain,
double_divide(X2,X) = double_divide(X,X2),
inference(substitution,[status(thm)],[c287]) ).
cnf(c289,plain,
inverse(double_divide(X2,X)) = inverse(double_divide(X,X2)),
inference(congruence,[status(thm)],[c288]) ).
cnf(c290,plain,
inverse(multiply(X,X2)) = double_divide(X,X2),
inference(substitution,[status(thm)],[c280]) ).
cnf(c291,plain,
double_divide(X,X2) = inverse(multiply(X,X2)),
inference(symmetry,[status(thm)],[c290]) ).
cnf(c292,plain,
inverse(double_divide(X,X2)) = inverse(inverse(multiply(X,X2))),
inference(congruence,[status(thm)],[c291]) ).
cnf(c293,plain,
inverse(inverse(multiply(X,X2))) = multiply(X,X2),
inference(substitution,[status(thm)],[c210]) ).
cnf(c294,plain,
multiply(X2,X) = multiply(X,X2),
inference(substitution,[status(thm)],[c255]) ).
cnf(c295,plain,
multiply(X,X2) = multiply(X2,X),
inference(symmetry,[status(thm)],[c294]) ).
cnf(c296,plain,
inverse(inverse(multiply(X,X2))) = multiply(X2,X),
inference(transitivity,[status(thm)],[c293,c295]) ).
cnf(c297,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c292,c296]) ).
cnf(c298,plain,
inverse(double_divide(X2,X)) = multiply(X2,X),
inference(transitivity,[status(thm)],[c289,c297]) ).
cnf(c299,plain,
inverse(double_divide(X,X2)) = multiply(X,X2),
inference(substitution,[status(thm)],[c298]) ).
cnf(c300,plain,
multiply(X,X2) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c299]) ).
cnf(c301,plain,
multiply(multiply(X,X2),inverse(X3)) = multiply(inverse(double_divide(X,X2)),inverse(X3)),
inference(congruence,[status(thm)],[c300]) ).
cnf(c302,plain,
double_divide(double_divide(X2,double_divide(double_divide(double_divide(X,X2),multiply(inverse(double_divide(X,X2)),inverse(X3))),inverse(X))),inverse(identity)) = multiply(inverse(double_divide(X,X2)),inverse(X3)),
inference(substitution,[status(thm)],[c44]) ).
cnf(c303,plain,
multiply(inverse(double_divide(X,X2)),inverse(X3)) = double_divide(double_divide(X2,double_divide(double_divide(double_divide(X,X2),multiply(inverse(double_divide(X,X2)),inverse(X3))),inverse(X))),inverse(identity)),
inference(symmetry,[status(thm)],[c302]) ).
cnf(c304,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c305,plain,
double_divide(X2,multiply(inverse(X2),inverse(X))) = double_divide(inverse(inverse(X2)),multiply(inverse(X2),inverse(X))),
inference(congruence,[status(thm)],[c304]) ).
cnf(c306,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c307,plain,
inverse(X) = inverse(inverse(inverse(X))),
inference(congruence,[status(thm)],[c306]) ).
cnf(c308,plain,
multiply(inverse(X2),inverse(X)) = multiply(inverse(inverse(inverse(X2))),inverse(X)),
inference(congruence,[status(thm)],[c307]) ).
cnf(c309,plain,
double_divide(inverse(inverse(X2)),multiply(inverse(X2),inverse(X))) = double_divide(inverse(inverse(X2)),multiply(inverse(inverse(inverse(X2))),inverse(X))),
inference(congruence,[status(thm)],[c308]) ).
cnf(c310,plain,
inverse(inverse(X)) = inverse(inverse(inverse(inverse(X)))),
inference(symmetry,[status(thm)],[c161]) ).
cnf(c311,plain,
double_divide(inverse(inverse(X2)),multiply(inverse(inverse(inverse(X2))),inverse(X))) = double_divide(inverse(inverse(inverse(inverse(X2)))),multiply(inverse(inverse(inverse(X2))),inverse(X))),
inference(congruence,[status(thm)],[c310]) ).
cnf(c312,plain,
double_divide(inverse(X2),multiply(X2,inverse(X))) = double_divide(multiply(X2,inverse(X)),inverse(X2)),
inference(substitution,[status(thm)],[c287]) ).
cnf(c313,plain,
inverse(inverse(double_divide(multiply(X2,inverse(X)),inverse(X2)))) = double_divide(multiply(X2,inverse(X)),inverse(X2)),
inference(substitution,[status(thm)],[c210]) ).
cnf(c314,plain,
double_divide(multiply(X2,inverse(X)),inverse(X2)) = inverse(inverse(double_divide(multiply(X2,inverse(X)),inverse(X2)))),
inference(symmetry,[status(thm)],[c313]) ).
cnf(c315,plain,
multiply(double_divide(multiply(X2,inverse(X)),inverse(X2)),identity) = inverse(inverse(double_divide(multiply(X2,inverse(X)),inverse(X2)))),
inference(substitution,[status(thm)],[c129]) ).
cnf(c316,plain,
inverse(inverse(double_divide(multiply(X2,inverse(X)),inverse(X2)))) = multiply(double_divide(multiply(X2,inverse(X)),inverse(X2)),identity),
inference(symmetry,[status(thm)],[c315]) ).
cnf(c317,plain,
double_divide(multiply(inverse(X2),multiply(X2,inverse(X))),inverse(identity)) = multiply(double_divide(multiply(X2,inverse(X)),inverse(X2)),identity),
inference(substitution,[status(thm)],[c136]) ).
cnf(c318,plain,
multiply(double_divide(multiply(X2,inverse(X)),inverse(X2)),identity) = double_divide(multiply(inverse(X2),multiply(X2,inverse(X))),inverse(identity)),
inference(symmetry,[status(thm)],[c317]) ).
cnf(c319,plain,
multiply(X2,inverse(X)) = multiply(inverse(X),X2),
inference(substitution,[status(thm)],[c255]) ).
cnf(c320,plain,
multiply(inverse(X2),multiply(X2,inverse(X))) = multiply(inverse(X2),multiply(inverse(X),X2)),
inference(congruence,[status(thm)],[c319]) ).
cnf(c321,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c322,plain,
double_divide(identity,X) = double_divide(identity,inverse(inverse(X))),
inference(congruence,[status(thm)],[c321]) ).
cnf(c323,plain,
inverse(inverse(inverse(X))) = inverse(X),
inference(substitution,[status(thm)],[c210]) ).
cnf(c324,plain,
double_divide(identity,inverse(inverse(X))) = inverse(X),
inference(transitivity,[status(thm)],[c240,c323]) ).
cnf(c325,plain,
double_divide(identity,X) = inverse(X),
inference(transitivity,[status(thm)],[c322,c324]) ).
cnf(c326,plain,
inverse(X) = double_divide(identity,X),
inference(symmetry,[status(thm)],[c325]) ).
cnf(c327,plain,
multiply(inverse(X),X2) = multiply(double_divide(identity,X),X2),
inference(congruence,[status(thm)],[c326]) ).
cnf(c328,plain,
multiply(inverse(X2),multiply(inverse(X),X2)) = multiply(inverse(X2),multiply(double_divide(identity,X),X2)),
inference(congruence,[status(thm)],[c327]) ).
cnf(c329,plain,
inverse(double_divide(multiply(double_divide(identity,X),X2),inverse(X2))) = multiply(inverse(X2),multiply(double_divide(identity,X),X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c330,plain,
multiply(inverse(X2),multiply(double_divide(identity,X),X2)) = inverse(double_divide(multiply(double_divide(identity,X),X2),inverse(X2))),
inference(symmetry,[status(thm)],[c329]) ).
cnf(c331,plain,
double_divide(multiply(double_divide(identity,X),X2),inverse(X2)) = inverse(inverse(X)),
inference(substitution,[status(thm)],[c150]) ).
cnf(c332,plain,
inverse(double_divide(multiply(double_divide(identity,X),X2),inverse(X2))) = inverse(inverse(inverse(X))),
inference(congruence,[status(thm)],[c331]) ).
cnf(c333,plain,
inverse(inverse(inverse(X))) = inverse(X),
inference(substitution,[status(thm)],[c210]) ).
cnf(c334,plain,
inverse(double_divide(multiply(double_divide(identity,X),X2),inverse(X2))) = inverse(X),
inference(transitivity,[status(thm)],[c332,c333]) ).
cnf(c335,plain,
multiply(inverse(X2),multiply(double_divide(identity,X),X2)) = inverse(X),
inference(transitivity,[status(thm)],[c330,c334]) ).
cnf(c336,plain,
multiply(inverse(X2),multiply(inverse(X),X2)) = inverse(X),
inference(transitivity,[status(thm)],[c328,c335]) ).
cnf(c337,plain,
multiply(inverse(X2),multiply(X2,inverse(X))) = inverse(X),
inference(transitivity,[status(thm)],[c320,c336]) ).
cnf(c338,plain,
double_divide(multiply(inverse(X2),multiply(X2,inverse(X))),inverse(identity)) = double_divide(inverse(X),inverse(identity)),
inference(congruence,[status(thm)],[c337]) ).
cnf(c339,plain,
multiply(X,identity) = X,
inference(transitivity,[status(thm)],[c129,c210]) ).
cnf(c340,plain,
double_divide(inverse(X),inverse(identity)) = X,
inference(transitivity,[status(thm)],[c51,c339]) ).
cnf(c341,plain,
double_divide(multiply(inverse(X2),multiply(X2,inverse(X))),inverse(identity)) = X,
inference(transitivity,[status(thm)],[c338,c340]) ).
cnf(c342,plain,
multiply(double_divide(multiply(X2,inverse(X)),inverse(X2)),identity) = X,
inference(transitivity,[status(thm)],[c318,c341]) ).
cnf(c343,plain,
inverse(inverse(double_divide(multiply(X2,inverse(X)),inverse(X2)))) = X,
inference(transitivity,[status(thm)],[c316,c342]) ).
cnf(c344,plain,
double_divide(multiply(X2,inverse(X)),inverse(X2)) = X,
inference(transitivity,[status(thm)],[c314,c343]) ).
cnf(c345,plain,
double_divide(inverse(X2),multiply(X2,inverse(X))) = X,
inference(transitivity,[status(thm)],[c312,c344]) ).
cnf(c346,plain,
double_divide(inverse(inverse(inverse(inverse(X2)))),multiply(inverse(inverse(inverse(X2))),inverse(X))) = X,
inference(substitution,[status(thm)],[c345]) ).
cnf(c347,plain,
double_divide(inverse(inverse(X2)),multiply(inverse(inverse(inverse(X2))),inverse(X))) = X,
inference(transitivity,[status(thm)],[c311,c346]) ).
cnf(c348,plain,
double_divide(inverse(inverse(X2)),multiply(inverse(X2),inverse(X))) = X,
inference(transitivity,[status(thm)],[c309,c347]) ).
cnf(c349,plain,
double_divide(X2,multiply(inverse(X2),inverse(X))) = X,
inference(transitivity,[status(thm)],[c305,c348]) ).
cnf(c350,plain,
double_divide(double_divide(X,X2),multiply(inverse(double_divide(X,X2)),inverse(X3))) = X3,
inference(substitution,[status(thm)],[c349]) ).
cnf(c351,plain,
double_divide(double_divide(double_divide(X,X2),multiply(inverse(double_divide(X,X2)),inverse(X3))),inverse(X)) = double_divide(X3,inverse(X)),
inference(congruence,[status(thm)],[c350]) ).
cnf(c352,plain,
double_divide(X2,double_divide(double_divide(double_divide(X,X2),multiply(inverse(double_divide(X,X2)),inverse(X3))),inverse(X))) = double_divide(X2,double_divide(X3,inverse(X))),
inference(congruence,[status(thm)],[c351]) ).
cnf(c353,plain,
double_divide(double_divide(X2,double_divide(double_divide(double_divide(X,X2),multiply(inverse(double_divide(X,X2)),inverse(X3))),inverse(X))),inverse(identity)) = double_divide(double_divide(X2,double_divide(X3,inverse(X))),inverse(identity)),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
multiply(X2,X) = multiply(X,X2),
inference(substitution,[status(thm)],[c255]) ).
cnf(c355,plain,
multiply(inverse(X2),multiply(X2,X)) = multiply(inverse(X2),multiply(X,X2)),
inference(congruence,[status(thm)],[c354]) ).
cnf(c356,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c357,plain,
multiply(X,X2) = multiply(inverse(inverse(X)),X2),
inference(congruence,[status(thm)],[c356]) ).
cnf(c358,plain,
multiply(inverse(X2),multiply(X,X2)) = multiply(inverse(X2),multiply(inverse(inverse(X)),X2)),
inference(congruence,[status(thm)],[c357]) ).
cnf(c359,plain,
multiply(inverse(inverse(X)),X2) = multiply(X2,inverse(inverse(X))),
inference(substitution,[status(thm)],[c255]) ).
cnf(c360,plain,
multiply(inverse(X2),multiply(inverse(inverse(X)),X2)) = multiply(inverse(X2),multiply(X2,inverse(inverse(X)))),
inference(congruence,[status(thm)],[c359]) ).
cnf(c361,plain,
multiply(inverse(X2),multiply(X2,inverse(inverse(X)))) = inverse(inverse(X)),
inference(substitution,[status(thm)],[c337]) ).
cnf(c362,plain,
multiply(inverse(X2),multiply(X2,inverse(inverse(X)))) = X,
inference(transitivity,[status(thm)],[c361,c210]) ).
cnf(c363,plain,
multiply(inverse(X2),multiply(inverse(inverse(X)),X2)) = X,
inference(transitivity,[status(thm)],[c360,c362]) ).
cnf(c364,plain,
multiply(inverse(X2),multiply(X,X2)) = X,
inference(transitivity,[status(thm)],[c358,c363]) ).
cnf(c365,plain,
multiply(inverse(X2),multiply(X2,X)) = X,
inference(transitivity,[status(thm)],[c355,c364]) ).
cnf(c366,plain,
multiply(inverse(X2),multiply(X2,double_divide(X2,inverse(X)))) = double_divide(X2,inverse(X)),
inference(substitution,[status(thm)],[c365]) ).
cnf(c367,plain,
double_divide(X2,inverse(X)) = multiply(inverse(X2),multiply(X2,double_divide(X2,inverse(X)))),
inference(symmetry,[status(thm)],[c366]) ).
cnf(c368,plain,
double_divide(X2,inverse(X)) = double_divide(inverse(X),X2),
inference(substitution,[status(thm)],[c287]) ).
cnf(c369,plain,
multiply(X2,double_divide(X2,inverse(X))) = multiply(X2,double_divide(inverse(X),X2)),
inference(congruence,[status(thm)],[c368]) ).
cnf(c370,plain,
inverse(double_divide(X2,double_divide(inverse(X),X2))) = multiply(X2,double_divide(inverse(X),X2)),
inference(substitution,[status(thm)],[c298]) ).
cnf(c371,plain,
multiply(X2,double_divide(inverse(X),X2)) = inverse(double_divide(X2,double_divide(inverse(X),X2))),
inference(symmetry,[status(thm)],[c370]) ).
cnf(c372,plain,
inverse(double_divide(X2,double_divide(inverse(X),X2))) = double_divide(double_divide(X2,double_divide(inverse(X),X2)),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c373,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c374,plain,
double_divide(double_divide(X2,double_divide(inverse(X),X2)),identity) = double_divide(double_divide(X2,double_divide(inverse(X),X2)),inverse(identity)),
inference(congruence,[status(thm)],[c373]) ).
cnf(c375,plain,
X = inverse(inverse(X)),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c376,plain,
double_divide(inverse(X),X2) = double_divide(inverse(X),inverse(inverse(X2))),
inference(congruence,[status(thm)],[c375]) ).
cnf(c377,plain,
double_divide(X2,double_divide(inverse(X),X2)) = double_divide(X2,double_divide(inverse(X),inverse(inverse(X2)))),
inference(congruence,[status(thm)],[c376]) ).
cnf(c378,plain,
double_divide(double_divide(X2,double_divide(inverse(X),X2)),inverse(identity)) = double_divide(double_divide(X2,double_divide(inverse(X),inverse(inverse(X2)))),inverse(identity)),
inference(congruence,[status(thm)],[c377]) ).
cnf(c379,plain,
inverse(X) = double_divide(identity,X),
inference(symmetry,[status(thm)],[c325]) ).
cnf(c380,plain,
double_divide(inverse(X),inverse(inverse(X2))) = double_divide(double_divide(identity,X),inverse(inverse(X2))),
inference(congruence,[status(thm)],[c379]) ).
cnf(c381,plain,
double_divide(X2,double_divide(inverse(X),inverse(inverse(X2)))) = double_divide(X2,double_divide(double_divide(identity,X),inverse(inverse(X2)))),
inference(congruence,[status(thm)],[c380]) ).
cnf(c382,plain,
double_divide(double_divide(X2,double_divide(inverse(X),inverse(inverse(X2)))),inverse(identity)) = double_divide(double_divide(X2,double_divide(double_divide(identity,X),inverse(inverse(X2)))),inverse(identity)),
inference(congruence,[status(thm)],[c381]) ).
cnf(c383,plain,
X2 = multiply(multiply(X2,double_divide(identity,X)),X),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c384,plain,
double_divide(inverse(X2),X2) = double_divide(inverse(X2),multiply(multiply(X2,double_divide(identity,X)),X)),
inference(congruence,[status(thm)],[c383]) ).
cnf(c385,plain,
X2 = multiply(multiply(X2,double_divide(identity,X)),X),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c386,plain,
inverse(X2) = inverse(multiply(multiply(X2,double_divide(identity,X)),X)),
inference(congruence,[status(thm)],[c385]) ).
cnf(c387,plain,
double_divide(inverse(X2),multiply(multiply(X2,double_divide(identity,X)),X)) = double_divide(inverse(multiply(multiply(X2,double_divide(identity,X)),X)),multiply(multiply(X2,double_divide(identity,X)),X)),
inference(congruence,[status(thm)],[c386]) ).
cnf(c388,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c389,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c388]) ).
cnf(c390,plain,
double_divide(inverse(multiply(X2,X)),multiply(X2,X)) = double_divide(inverse(multiply(X2,X)),inverse(double_divide(X,X2))),
inference(congruence,[status(thm)],[c389]) ).
cnf(c391,plain,
inverse(double_divide(X,X2)) = multiply(X2,X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c392,plain,
multiply(X2,X) = inverse(double_divide(X,X2)),
inference(symmetry,[status(thm)],[c391]) ).
cnf(c393,plain,
inverse(multiply(X2,X)) = inverse(inverse(double_divide(X,X2))),
inference(congruence,[status(thm)],[c392]) ).
cnf(c394,plain,
double_divide(inverse(multiply(X2,X)),inverse(double_divide(X,X2))) = double_divide(inverse(inverse(double_divide(X,X2))),inverse(double_divide(X,X2))),
inference(congruence,[status(thm)],[c393]) ).
cnf(c395,plain,
inverse(inverse(X)) = multiply(identity,X),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c396,plain,
double_divide(inverse(inverse(X)),inverse(X)) = double_divide(multiply(identity,X),inverse(X)),
inference(congruence,[status(thm)],[c395]) ).
cnf(c397,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c398,plain,
multiply(identity,X) = multiply(inverse(identity),X),
inference(congruence,[status(thm)],[c397]) ).
cnf(c399,plain,
double_divide(multiply(identity,X),inverse(X)) = double_divide(multiply(inverse(identity),X),inverse(X)),
inference(congruence,[status(thm)],[c398]) ).
cnf(c400,plain,
inverse(identity) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c401,plain,
multiply(inverse(identity),X) = multiply(double_divide(identity,identity),X),
inference(congruence,[status(thm)],[c400]) ).
cnf(c402,plain,
double_divide(multiply(inverse(identity),X),inverse(X)) = double_divide(multiply(double_divide(identity,identity),X),inverse(X)),
inference(congruence,[status(thm)],[c401]) ).
cnf(c403,plain,
double_divide(multiply(double_divide(identity,identity),X),inverse(X)) = inverse(inverse(identity)),
inference(substitution,[status(thm)],[c150]) ).
cnf(c404,plain,
inverse(inverse(identity)) = inverse(identity),
inference(congruence,[status(thm)],[c89]) ).
cnf(c405,plain,
inverse(inverse(identity)) = identity,
inference(transitivity,[status(thm)],[c404,c89]) ).
cnf(c406,plain,
double_divide(multiply(double_divide(identity,identity),X),inverse(X)) = identity,
inference(transitivity,[status(thm)],[c403,c405]) ).
cnf(c407,plain,
double_divide(multiply(inverse(identity),X),inverse(X)) = identity,
inference(transitivity,[status(thm)],[c402,c406]) ).
cnf(c408,plain,
double_divide(multiply(identity,X),inverse(X)) = identity,
inference(transitivity,[status(thm)],[c399,c407]) ).
cnf(c409,plain,
double_divide(inverse(inverse(X)),inverse(X)) = identity,
inference(transitivity,[status(thm)],[c396,c408]) ).
cnf(c410,plain,
double_divide(inverse(inverse(double_divide(X,X2))),inverse(double_divide(X,X2))) = identity,
inference(substitution,[status(thm)],[c409]) ).
cnf(c411,plain,
double_divide(inverse(multiply(X2,X)),inverse(double_divide(X,X2))) = identity,
inference(transitivity,[status(thm)],[c394,c410]) ).
cnf(c412,plain,
double_divide(inverse(multiply(X2,X)),multiply(X2,X)) = identity,
inference(transitivity,[status(thm)],[c390,c411]) ).
cnf(c413,plain,
double_divide(inverse(multiply(multiply(X2,double_divide(identity,X)),X)),multiply(multiply(X2,double_divide(identity,X)),X)) = identity,
inference(substitution,[status(thm)],[c412]) ).
cnf(c414,plain,
double_divide(inverse(X2),multiply(multiply(X2,double_divide(identity,X)),X)) = identity,
inference(transitivity,[status(thm)],[c387,c413]) ).
cnf(c415,plain,
double_divide(inverse(X),X) = identity,
inference(transitivity,[status(thm)],[c384,c414]) ).
cnf(c416,plain,
identity = double_divide(inverse(X),X),
inference(symmetry,[status(thm)],[c415]) ).
cnf(c417,plain,
double_divide(identity,X) = double_divide(double_divide(inverse(X2),X2),X),
inference(congruence,[status(thm)],[c416]) ).
cnf(c418,plain,
double_divide(double_divide(identity,X),inverse(inverse(X2))) = double_divide(double_divide(double_divide(inverse(X2),X2),X),inverse(inverse(X2))),
inference(congruence,[status(thm)],[c417]) ).
cnf(c419,plain,
double_divide(X2,double_divide(double_divide(identity,X),inverse(inverse(X2)))) = double_divide(X2,double_divide(double_divide(double_divide(inverse(X2),X2),X),inverse(inverse(X2)))),
inference(congruence,[status(thm)],[c418]) ).
cnf(c420,plain,
double_divide(double_divide(X2,double_divide(double_divide(identity,X),inverse(inverse(X2)))),inverse(identity)) = double_divide(double_divide(X2,double_divide(double_divide(double_divide(inverse(X2),X2),X),inverse(inverse(X2)))),inverse(identity)),
inference(congruence,[status(thm)],[c419]) ).
cnf(c421,plain,
double_divide(double_divide(X2,double_divide(double_divide(double_divide(inverse(X2),X2),X),inverse(inverse(X2)))),inverse(identity)) = X,
inference(substitution,[status(thm)],[c44]) ).
cnf(c422,plain,
double_divide(double_divide(X2,double_divide(double_divide(identity,X),inverse(inverse(X2)))),inverse(identity)) = X,
inference(transitivity,[status(thm)],[c420,c421]) ).
cnf(c423,plain,
double_divide(double_divide(X2,double_divide(inverse(X),inverse(inverse(X2)))),inverse(identity)) = X,
inference(transitivity,[status(thm)],[c382,c422]) ).
cnf(c424,plain,
double_divide(double_divide(X2,double_divide(inverse(X),X2)),inverse(identity)) = X,
inference(transitivity,[status(thm)],[c378,c423]) ).
cnf(c425,plain,
double_divide(double_divide(X2,double_divide(inverse(X),X2)),identity) = X,
inference(transitivity,[status(thm)],[c374,c424]) ).
cnf(c426,plain,
inverse(double_divide(X2,double_divide(inverse(X),X2))) = X,
inference(transitivity,[status(thm)],[c372,c425]) ).
cnf(c427,plain,
multiply(X2,double_divide(inverse(X),X2)) = X,
inference(transitivity,[status(thm)],[c371,c426]) ).
cnf(c428,plain,
multiply(X2,double_divide(X2,inverse(X))) = X,
inference(transitivity,[status(thm)],[c369,c427]) ).
cnf(c429,plain,
multiply(inverse(X2),multiply(X2,double_divide(X2,inverse(X)))) = multiply(inverse(X2),X),
inference(congruence,[status(thm)],[c428]) ).
cnf(c430,plain,
multiply(X,inverse(X2)) = multiply(inverse(X2),X),
inference(substitution,[status(thm)],[c255]) ).
cnf(c431,plain,
multiply(inverse(X2),X) = multiply(X,inverse(X2)),
inference(symmetry,[status(thm)],[c430]) ).
cnf(c432,plain,
multiply(inverse(X2),multiply(X2,double_divide(X2,inverse(X)))) = multiply(X,inverse(X2)),
inference(transitivity,[status(thm)],[c429,c431]) ).
cnf(c433,plain,
double_divide(X2,inverse(X)) = multiply(X,inverse(X2)),
inference(transitivity,[status(thm)],[c367,c432]) ).
cnf(c434,plain,
double_divide(double_divide(X2,double_divide(X3,inverse(X))),inverse(identity)) = multiply(identity,inverse(double_divide(X2,double_divide(X3,inverse(X))))),
inference(substitution,[status(thm)],[c433]) ).
cnf(c435,plain,
multiply(identity,inverse(double_divide(X2,double_divide(X3,inverse(X))))) = inverse(inverse(inverse(double_divide(X2,double_divide(X3,inverse(X)))))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c436,plain,
inverse(inverse(inverse(double_divide(X2,double_divide(X3,inverse(X)))))) = inverse(double_divide(X2,double_divide(X3,inverse(X)))),
inference(substitution,[status(thm)],[c210]) ).
cnf(c437,plain,
inverse(double_divide(X2,double_divide(X3,inverse(X)))) = multiply(X2,double_divide(X3,inverse(X))),
inference(substitution,[status(thm)],[c298]) ).
cnf(c438,plain,
multiply(X2,double_divide(X3,inverse(X))) = multiply(X2,multiply(X,inverse(X3))),
inference(congruence,[status(thm)],[c433]) ).
cnf(c439,plain,
inverse(double_divide(X2,double_divide(X3,inverse(X)))) = multiply(X2,multiply(X,inverse(X3))),
inference(transitivity,[status(thm)],[c437,c438]) ).
cnf(c440,plain,
inverse(inverse(inverse(double_divide(X2,double_divide(X3,inverse(X)))))) = multiply(X2,multiply(X,inverse(X3))),
inference(transitivity,[status(thm)],[c436,c439]) ).
cnf(c441,plain,
multiply(identity,inverse(double_divide(X2,double_divide(X3,inverse(X))))) = multiply(X2,multiply(X,inverse(X3))),
inference(transitivity,[status(thm)],[c435,c440]) ).
cnf(c442,plain,
double_divide(double_divide(X2,double_divide(X3,inverse(X))),inverse(identity)) = multiply(X2,multiply(X,inverse(X3))),
inference(transitivity,[status(thm)],[c434,c441]) ).
cnf(c443,plain,
double_divide(double_divide(X2,double_divide(double_divide(double_divide(X,X2),multiply(inverse(double_divide(X,X2)),inverse(X3))),inverse(X))),inverse(identity)) = multiply(X2,multiply(X,inverse(X3))),
inference(transitivity,[status(thm)],[c353,c442]) ).
cnf(c444,plain,
multiply(inverse(double_divide(X,X2)),inverse(X3)) = multiply(X2,multiply(X,inverse(X3))),
inference(transitivity,[status(thm)],[c303,c443]) ).
cnf(c445,plain,
multiply(multiply(X,X2),inverse(X3)) = multiply(X2,multiply(X,inverse(X3))),
inference(transitivity,[status(thm)],[c301,c444]) ).
cnf(c446,plain,
multiply(inverse(inverse(inverse(X3))),multiply(X,X2)) = multiply(X2,multiply(X,inverse(X3))),
inference(transitivity,[status(thm)],[c267,c445]) ).
cnf(c447,plain,
multiply(inverse(X3),multiply(X,X2)) = multiply(X2,multiply(X,inverse(X3))),
inference(transitivity,[status(thm)],[c266,c446]) ).
cnf(c448,plain,
multiply(inverse(X3),multiply(X2,X)) = multiply(X2,multiply(X,inverse(X3))),
inference(transitivity,[status(thm)],[c263,c447]) ).
cnf(c449,plain,
multiply(inverse(inverse(inverse(inverse(X)))),multiply(X3,X2)) = multiply(X3,multiply(X2,inverse(inverse(inverse(inverse(X)))))),
inference(substitution,[status(thm)],[c448]) ).
cnf(c450,plain,
double_divide(double_divide(X2,double_divide(identity,inverse(inverse(inverse(inverse(X)))))),inverse(identity)) = multiply(X2,inverse(inverse(inverse(X)))),
inference(substitution,[status(thm)],[c48]) ).
cnf(c451,plain,
multiply(X2,inverse(inverse(inverse(X)))) = double_divide(double_divide(X2,double_divide(identity,inverse(inverse(inverse(inverse(X)))))),inverse(identity)),
inference(symmetry,[status(thm)],[c450]) ).
cnf(c452,plain,
double_divide(identity,inverse(inverse(inverse(inverse(X))))) = double_divide(identity,inverse(inverse(X))),
inference(congruence,[status(thm)],[c161]) ).
cnf(c453,plain,
double_divide(X2,double_divide(identity,inverse(inverse(inverse(inverse(X)))))) = double_divide(X2,double_divide(identity,inverse(inverse(X)))),
inference(congruence,[status(thm)],[c452]) ).
cnf(c454,plain,
double_divide(double_divide(X2,double_divide(identity,inverse(inverse(inverse(inverse(X)))))),inverse(identity)) = double_divide(double_divide(X2,double_divide(identity,inverse(inverse(X)))),inverse(identity)),
inference(congruence,[status(thm)],[c453]) ).
cnf(c455,plain,
double_divide(double_divide(X2,double_divide(identity,inverse(inverse(X)))),inverse(identity)) = multiply(X2,inverse(X)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c456,plain,
double_divide(double_divide(X2,double_divide(identity,inverse(inverse(inverse(inverse(X)))))),inverse(identity)) = multiply(X2,inverse(X)),
inference(transitivity,[status(thm)],[c454,c455]) ).
cnf(c457,plain,
multiply(X2,inverse(inverse(inverse(X)))) = multiply(X2,inverse(X)),
inference(transitivity,[status(thm)],[c451,c456]) ).
cnf(c458,plain,
multiply(X2,inverse(inverse(inverse(inverse(X))))) = multiply(X2,inverse(inverse(X))),
inference(substitution,[status(thm)],[c457]) ).
cnf(c459,plain,
multiply(X3,multiply(X2,inverse(inverse(inverse(inverse(X)))))) = multiply(X3,multiply(X2,inverse(inverse(X)))),
inference(congruence,[status(thm)],[c458]) ).
cnf(c460,plain,
multiply(X2,inverse(inverse(X))) = multiply(X2,X),
inference(congruence,[status(thm)],[c210]) ).
cnf(c461,plain,
multiply(X3,multiply(X2,inverse(inverse(X)))) = multiply(X3,multiply(X2,X)),
inference(congruence,[status(thm)],[c460]) ).
cnf(c462,plain,
multiply(X3,multiply(X2,inverse(inverse(inverse(inverse(X)))))) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c459,c461]) ).
cnf(c463,plain,
multiply(inverse(inverse(inverse(inverse(X)))),multiply(X3,X2)) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c449,c462]) ).
cnf(c464,plain,
multiply(inverse(inverse(X)),multiply(X3,X2)) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c261,c463]) ).
cnf(c465,plain,
multiply(X,multiply(X3,X2)) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c259,c464]) ).
cnf(c466,plain,
multiply(c3,multiply(a3,b3)) = multiply(a3,multiply(b3,c3)),
inference(substitution,[status(thm)],[c465]) ).
cnf(c467,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(transitivity,[status(thm)],[c257,c466]) ).
cnf(c468,plain,
$false,
inference(resolution,[status(thm)],[c1,c467]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP579-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n004.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 10:07:51 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.52 Command-line arguments: --no-flatten-goal
% 0.20/0.52
% 0.20/0.52 % SZS status Unsatisfiable
% 0.20/0.52
% 0.20/0.54 % SZS output start CNFRefutation
% See solution above
% 1.91/0.75
% 1.91/0.75 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------