Twee---2.7.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : GRP582-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n018.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 0.13s 0.46s
% Output   : CNFRefutation 1.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :  112
%            Number of leaves      :    5
% Syntax   : Number of clauses     :  412 ( 412 unt;   0 nHn;  55 RR)
%            Number of literals    :  412 ( 411 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   12 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  502 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
    multiply(identity,a2) != a2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).

cnf(c2,axiom,
    identity = double_divide(A,inverse(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).

cnf(c3,plain,
    identity = double_divide(X,inverse(X)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c4,plain,
    multiply(identity,X) = multiply(double_divide(X,inverse(X)),X),
    inference(congruence,[status(thm)],[c3]) ).

cnf(c5,axiom,
    double_divide(double_divide(A2,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A2)))),double_divide(identity,identity)) = C,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).

cnf(c6,plain,
    double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),double_divide(identity,identity))),double_divide(identity,identity)))),double_divide(identity,identity)) = double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),double_divide(identity,identity))),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c7,plain,
    double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),double_divide(identity,identity))) = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),double_divide(identity,identity))),double_divide(identity,identity)))),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c6]) ).

cnf(c8,axiom,
    inverse(A2) = double_divide(A2,identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).

cnf(c9,plain,
    inverse(X) = double_divide(X,identity),
    inference(substitution,[status(thm)],[c8]) ).

cnf(c10,plain,
    double_divide(X,identity) = inverse(X),
    inference(symmetry,[status(thm)],[c9]) ).

cnf(c11,plain,
    double_divide(double_divide(identity,X2),double_divide(X,identity)) = double_divide(double_divide(identity,X2),inverse(X)),
    inference(congruence,[status(thm)],[c10]) ).

cnf(c12,plain,
    double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),double_divide(X,identity))) = double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),inverse(X))),
    inference(congruence,[status(thm)],[c11]) ).

cnf(c13,plain,
    double_divide(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),double_divide(X,identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),inverse(X))),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c12]) ).

cnf(c14,plain,
    inverse(X) = double_divide(X,identity),
    inference(substitution,[status(thm)],[c8]) ).

cnf(c15,plain,
    double_divide(double_divide(identity,X2),inverse(X)) = double_divide(double_divide(identity,X2),double_divide(X,identity)),
    inference(congruence,[status(thm)],[c14]) ).

cnf(c16,plain,
    double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),inverse(X))) = double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),double_divide(X,identity))),
    inference(congruence,[status(thm)],[c15]) ).

cnf(c17,plain,
    double_divide(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),inverse(X))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),double_divide(X,identity))),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c16]) ).

cnf(c18,plain,
    inverse(X) = double_divide(X,identity),
    inference(substitution,[status(thm)],[c8]) ).

cnf(c19,plain,
    double_divide(X,identity) = inverse(X),
    inference(symmetry,[status(thm)],[c18]) ).

cnf(c20,plain,
    double_divide(X,double_divide(X,identity)) = double_divide(X,inverse(X)),
    inference(congruence,[status(thm)],[c19]) ).

cnf(c21,plain,
    identity = double_divide(X,inverse(X)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c22,plain,
    double_divide(X,inverse(X)) = identity,
    inference(symmetry,[status(thm)],[c21]) ).

cnf(c23,plain,
    double_divide(X,double_divide(X,identity)) = identity,
    inference(transitivity,[status(thm)],[c20,c22]) ).

cnf(c24,plain,
    identity = double_divide(X,double_divide(X,identity)),
    inference(symmetry,[status(thm)],[c23]) ).

cnf(c25,plain,
    double_divide(X,identity) = double_divide(X,double_divide(X2,double_divide(X2,identity))),
    inference(congruence,[status(thm)],[c24]) ).

cnf(c26,plain,
    double_divide(double_divide(identity,X2),double_divide(X,identity)) = double_divide(double_divide(identity,X2),double_divide(X,double_divide(X2,double_divide(X2,identity)))),
    inference(congruence,[status(thm)],[c25]) ).

cnf(c27,plain,
    double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),double_divide(X,identity))) = double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),double_divide(X,double_divide(X2,double_divide(X2,identity))))),
    inference(congruence,[status(thm)],[c26]) ).

cnf(c28,plain,
    double_divide(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),double_divide(X,identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),double_divide(X,double_divide(X2,double_divide(X2,identity))))),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c27]) ).

cnf(c29,plain,
    double_divide(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),double_divide(X,double_divide(X2,double_divide(X2,identity))))),double_divide(identity,identity)) = X,
    inference(substitution,[status(thm)],[c5]) ).

cnf(c30,plain,
    double_divide(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),double_divide(X,identity))),double_divide(identity,identity)) = X,
    inference(transitivity,[status(thm)],[c28,c29]) ).

cnf(c31,plain,
    double_divide(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),inverse(X))),double_divide(identity,identity)) = X,
    inference(transitivity,[status(thm)],[c17,c30]) ).

cnf(c32,plain,
    double_divide(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),double_divide(X,identity))),double_divide(identity,identity)) = X,
    inference(transitivity,[status(thm)],[c13,c31]) ).

cnf(c33,plain,
    double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),double_divide(identity,identity))),double_divide(identity,identity)) = identity,
    inference(substitution,[status(thm)],[c32]) ).

cnf(c34,plain,
    double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),double_divide(identity,identity))),double_divide(identity,identity))) = double_divide(double_divide(identity,identity),identity),
    inference(congruence,[status(thm)],[c33]) ).

cnf(c35,plain,
    double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),double_divide(identity,identity))),double_divide(identity,identity)))) = double_divide(identity,double_divide(double_divide(identity,identity),identity)),
    inference(congruence,[status(thm)],[c34]) ).

cnf(c36,plain,
    double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),double_divide(identity,identity))),double_divide(identity,identity)))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),identity)),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c35]) ).

cnf(c37,plain,
    inverse(double_divide(identity,identity)) = double_divide(double_divide(identity,identity),identity),
    inference(substitution,[status(thm)],[c8]) ).

cnf(c38,plain,
    double_divide(double_divide(identity,identity),identity) = inverse(double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c37]) ).

cnf(c39,plain,
    double_divide(identity,double_divide(double_divide(identity,identity),identity)) = double_divide(identity,inverse(double_divide(identity,identity))),
    inference(congruence,[status(thm)],[c38]) ).

cnf(c40,plain,
    double_divide(double_divide(identity,double_divide(double_divide(identity,identity),identity)),double_divide(identity,identity)) = double_divide(double_divide(identity,inverse(double_divide(identity,identity))),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c39]) ).

cnf(c41,plain,
    inverse(double_divide(identity,X)) = double_divide(double_divide(identity,X),identity),
    inference(substitution,[status(thm)],[c8]) ).

cnf(c42,plain,
    double_divide(identity,inverse(double_divide(identity,X))) = double_divide(identity,double_divide(double_divide(identity,X),identity)),
    inference(congruence,[status(thm)],[c41]) ).

cnf(c43,plain,
    double_divide(double_divide(identity,inverse(double_divide(identity,X))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(identity,X),identity)),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c42]) ).

cnf(c44,plain,
    identity = double_divide(X,double_divide(X,identity)),
    inference(symmetry,[status(thm)],[c23]) ).

cnf(c45,plain,
    double_divide(double_divide(identity,X),identity) = double_divide(double_divide(identity,X),double_divide(X,double_divide(X,identity))),
    inference(congruence,[status(thm)],[c44]) ).

cnf(c46,plain,
    double_divide(identity,double_divide(double_divide(identity,X),identity)) = double_divide(identity,double_divide(double_divide(identity,X),double_divide(X,double_divide(X,identity)))),
    inference(congruence,[status(thm)],[c45]) ).

cnf(c47,plain,
    double_divide(double_divide(identity,double_divide(double_divide(identity,X),identity)),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(identity,X),double_divide(X,double_divide(X,identity)))),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c46]) ).

cnf(c48,plain,
    double_divide(double_divide(identity,double_divide(double_divide(identity,X),double_divide(X,double_divide(X,identity)))),double_divide(identity,identity)) = X,
    inference(substitution,[status(thm)],[c5]) ).

cnf(c49,plain,
    double_divide(double_divide(identity,double_divide(double_divide(identity,X),identity)),double_divide(identity,identity)) = X,
    inference(transitivity,[status(thm)],[c47,c48]) ).

cnf(c50,plain,
    double_divide(double_divide(identity,inverse(double_divide(identity,X))),double_divide(identity,identity)) = X,
    inference(transitivity,[status(thm)],[c43,c49]) ).

cnf(c51,plain,
    double_divide(double_divide(identity,inverse(double_divide(identity,identity))),double_divide(identity,identity)) = identity,
    inference(substitution,[status(thm)],[c50]) ).

cnf(c52,plain,
    double_divide(double_divide(identity,double_divide(double_divide(identity,identity),identity)),double_divide(identity,identity)) = identity,
    inference(transitivity,[status(thm)],[c40,c51]) ).

cnf(c53,plain,
    double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),double_divide(identity,identity))),double_divide(identity,identity)))),double_divide(identity,identity)) = identity,
    inference(transitivity,[status(thm)],[c36,c52]) ).

cnf(c54,plain,
    double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),double_divide(identity,identity))) = identity,
    inference(transitivity,[status(thm)],[c7,c53]) ).

cnf(c55,plain,
    double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),double_divide(identity,identity))) = identity,
    inference(substitution,[status(thm)],[c54]) ).

cnf(c56,plain,
    identity = double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),double_divide(identity,identity))),
    inference(symmetry,[status(thm)],[c55]) ).

cnf(c57,plain,
    double_divide(identity,identity) = double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),double_divide(identity,identity)))),
    inference(congruence,[status(thm)],[c56]) ).

cnf(c58,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),double_divide(identity,identity)))),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c57]) ).

cnf(c59,plain,
    double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),double_divide(identity,identity)))),double_divide(identity,identity)) = double_divide(identity,identity),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c60,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(identity,identity),
    inference(transitivity,[status(thm)],[c58,c59]) ).

cnf(c61,plain,
    double_divide(identity,identity) = double_divide(double_divide(identity,identity),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c60]) ).

cnf(c62,plain,
    double_divide(identity,identity) = double_divide(double_divide(identity,identity),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c60]) ).

cnf(c63,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c62]) ).

cnf(c64,plain,
    double_divide(identity,identity) = double_divide(double_divide(identity,identity),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c60]) ).

cnf(c65,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),double_divide(identity,identity))),
    inference(congruence,[status(thm)],[c64]) ).

cnf(c66,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),double_divide(identity,identity))),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c65]) ).

cnf(c67,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),double_divide(identity,identity))),double_divide(identity,identity)) = identity,
    inference(substitution,[status(thm)],[c32]) ).

cnf(c68,plain,
    double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),double_divide(identity,identity)) = identity,
    inference(transitivity,[status(thm)],[c66,c67]) ).

cnf(c69,plain,
    double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
    inference(transitivity,[status(thm)],[c63,c68]) ).

cnf(c70,plain,
    double_divide(identity,identity) = identity,
    inference(transitivity,[status(thm)],[c61,c69]) ).

cnf(c71,plain,
    double_divide(X,double_divide(identity,identity)) = double_divide(X,identity),
    inference(congruence,[status(thm)],[c70]) ).

cnf(c72,plain,
    inverse(X) = double_divide(X,identity),
    inference(substitution,[status(thm)],[c8]) ).

cnf(c73,plain,
    double_divide(X,identity) = inverse(X),
    inference(symmetry,[status(thm)],[c72]) ).

cnf(c74,plain,
    double_divide(X,double_divide(identity,identity)) = inverse(X),
    inference(transitivity,[status(thm)],[c71,c73]) ).

cnf(c75,plain,
    inverse(X) = double_divide(X,double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c74]) ).

cnf(c76,plain,
    double_divide(X2,inverse(X)) = double_divide(X2,double_divide(X,double_divide(identity,identity))),
    inference(congruence,[status(thm)],[c75]) ).

cnf(c77,plain,
    multiply(double_divide(X2,inverse(X)),X2) = multiply(double_divide(X2,double_divide(X,double_divide(identity,identity))),X2),
    inference(congruence,[status(thm)],[c76]) ).

cnf(c78,plain,
    inverse(double_divide(X2,X)) = double_divide(double_divide(X2,X),identity),
    inference(substitution,[status(thm)],[c8]) ).

cnf(c79,axiom,
    multiply(A2,B2) = double_divide(double_divide(B2,A2),identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).

cnf(c80,plain,
    multiply(X,X2) = double_divide(double_divide(X2,X),identity),
    inference(substitution,[status(thm)],[c79]) ).

cnf(c81,plain,
    double_divide(double_divide(X2,X),identity) = multiply(X,X2),
    inference(symmetry,[status(thm)],[c80]) ).

cnf(c82,plain,
    inverse(double_divide(X2,X)) = multiply(X,X2),
    inference(transitivity,[status(thm)],[c78,c81]) ).

cnf(c83,plain,
    inverse(double_divide(X,X2)) = multiply(X2,X),
    inference(substitution,[status(thm)],[c82]) ).

cnf(c84,plain,
    multiply(X2,X) = inverse(double_divide(X,X2)),
    inference(symmetry,[status(thm)],[c83]) ).

cnf(c85,plain,
    inverse(multiply(X2,X)) = inverse(inverse(double_divide(X,X2))),
    inference(congruence,[status(thm)],[c84]) ).

cnf(c86,plain,
    inverse(inverse(multiply(X2,X))) = inverse(inverse(inverse(double_divide(X,X2)))),
    inference(congruence,[status(thm)],[c85]) ).

cnf(c87,plain,
    inverse(inverse(inverse(multiply(X2,X)))) = inverse(inverse(inverse(inverse(double_divide(X,X2))))),
    inference(congruence,[status(thm)],[c86]) ).

cnf(c88,plain,
    inverse(inverse(inverse(inverse(multiply(X2,X))))) = inverse(inverse(inverse(inverse(inverse(double_divide(X,X2)))))),
    inference(congruence,[status(thm)],[c87]) ).

cnf(c89,plain,
    inverse(inverse(inverse(inverse(inverse(multiply(X2,X)))))) = inverse(inverse(inverse(inverse(inverse(inverse(double_divide(X,X2))))))),
    inference(congruence,[status(thm)],[c88]) ).

cnf(c90,plain,
    inverse(inverse(inverse(inverse(inverse(inverse(multiply(X2,X))))))) = inverse(inverse(inverse(inverse(inverse(inverse(inverse(double_divide(X,X2)))))))),
    inference(congruence,[status(thm)],[c89]) ).

cnf(c91,plain,
    inverse(double_divide(double_divide(identity,identity),X)) = multiply(X,double_divide(identity,identity)),
    inference(substitution,[status(thm)],[c82]) ).

cnf(c92,plain,
    multiply(X,double_divide(identity,identity)) = inverse(double_divide(double_divide(identity,identity),X)),
    inference(symmetry,[status(thm)],[c91]) ).

cnf(c93,plain,
    double_divide(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)),double_divide(identity,identity)) = inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))),
    inference(substitution,[status(thm)],[c74]) ).

cnf(c94,plain,
    inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))) = double_divide(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c93]) ).

cnf(c95,plain,
    double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),inverse(X))),double_divide(identity,identity)))),double_divide(identity,identity)) = double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),inverse(X))),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c96,plain,
    double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),inverse(X))) = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),inverse(X))),double_divide(identity,identity)))),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c95]) ).

cnf(c97,plain,
    double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),inverse(X))),double_divide(identity,identity))) = double_divide(double_divide(identity,identity),X),
    inference(congruence,[status(thm)],[c31]) ).

cnf(c98,plain,
    double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),inverse(X))),double_divide(identity,identity)))) = double_divide(identity,double_divide(double_divide(identity,identity),X)),
    inference(congruence,[status(thm)],[c97]) ).

cnf(c99,plain,
    double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),inverse(X))),double_divide(identity,identity)))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),X)),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c98]) ).

cnf(c100,plain,
    double_divide(double_divide(identity,double_divide(double_divide(identity,identity),X)),double_divide(identity,identity)) = inverse(double_divide(identity,double_divide(double_divide(identity,identity),X))),
    inference(substitution,[status(thm)],[c74]) ).

cnf(c101,plain,
    inverse(double_divide(identity,double_divide(double_divide(identity,identity),X))) = multiply(double_divide(double_divide(identity,identity),X),identity),
    inference(substitution,[status(thm)],[c82]) ).

cnf(c102,plain,
    identity = double_divide(identity,identity),
    inference(symmetry,[status(thm)],[c70]) ).

cnf(c103,plain,
    multiply(double_divide(double_divide(identity,identity),X),identity) = multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c102]) ).

cnf(c104,plain,
    inverse(double_divide(identity,double_divide(double_divide(identity,identity),X))) = multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)),
    inference(transitivity,[status(thm)],[c101,c103]) ).

cnf(c105,plain,
    double_divide(double_divide(identity,double_divide(double_divide(identity,identity),X)),double_divide(identity,identity)) = multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)),
    inference(transitivity,[status(thm)],[c100,c104]) ).

cnf(c106,plain,
    double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),inverse(X))),double_divide(identity,identity)))),double_divide(identity,identity)) = multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)),
    inference(transitivity,[status(thm)],[c99,c105]) ).

cnf(c107,plain,
    double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),inverse(X))) = multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)),
    inference(transitivity,[status(thm)],[c96,c106]) ).

cnf(c108,plain,
    double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),inverse(X2))) = multiply(double_divide(double_divide(identity,identity),X2),double_divide(identity,identity)),
    inference(substitution,[status(thm)],[c107]) ).

cnf(c109,plain,
    multiply(double_divide(double_divide(identity,identity),X2),double_divide(identity,identity)) = double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),inverse(X2))),
    inference(symmetry,[status(thm)],[c108]) ).

cnf(c110,plain,
    double_divide(multiply(double_divide(double_divide(identity,identity),X2),double_divide(identity,identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),inverse(X2))),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c109]) ).

cnf(c111,plain,
    double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),inverse(X2))),double_divide(identity,identity)) = X2,
    inference(substitution,[status(thm)],[c31]) ).

cnf(c112,plain,
    double_divide(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)),double_divide(identity,identity)) = X,
    inference(transitivity,[status(thm)],[c110,c111]) ).

cnf(c113,plain,
    inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))) = X,
    inference(transitivity,[status(thm)],[c94,c112]) ).

cnf(c114,plain,
    inverse(multiply(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),X)),double_divide(identity,identity))) = double_divide(double_divide(identity,identity),X),
    inference(substitution,[status(thm)],[c113]) ).

cnf(c115,plain,
    double_divide(double_divide(identity,identity),X) = inverse(multiply(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),X)),double_divide(identity,identity))),
    inference(symmetry,[status(thm)],[c114]) ).

cnf(c116,plain,
    double_divide(double_divide(identity,identity),X) = double_divide(identity,X),
    inference(congruence,[status(thm)],[c70]) ).

cnf(c117,plain,
    double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),X)) = double_divide(double_divide(identity,identity),double_divide(identity,X)),
    inference(congruence,[status(thm)],[c116]) ).

cnf(c118,plain,
    multiply(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),X)),double_divide(identity,identity)) = multiply(double_divide(double_divide(identity,identity),double_divide(identity,X)),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c117]) ).

cnf(c119,plain,
    double_divide(double_divide(X,double_divide(double_divide(identity,identity),double_divide(multiply(double_divide(double_divide(identity,identity),double_divide(identity,X)),double_divide(identity,identity)),double_divide(identity,X)))),double_divide(identity,identity)) = multiply(double_divide(double_divide(identity,identity),double_divide(identity,X)),double_divide(identity,identity)),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c120,plain,
    multiply(double_divide(double_divide(identity,identity),double_divide(identity,X)),double_divide(identity,identity)) = double_divide(double_divide(X,double_divide(double_divide(identity,identity),double_divide(multiply(double_divide(double_divide(identity,identity),double_divide(identity,X)),double_divide(identity,identity)),double_divide(identity,X)))),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c119]) ).

cnf(c121,plain,
    X = inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))),
    inference(symmetry,[status(thm)],[c113]) ).

cnf(c122,plain,
    double_divide(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)),X) = double_divide(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)),inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)))),
    inference(congruence,[status(thm)],[c121]) ).

cnf(c123,plain,
    identity = double_divide(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)),inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c124,plain,
    double_divide(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)),inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)))) = identity,
    inference(symmetry,[status(thm)],[c123]) ).

cnf(c125,plain,
    identity = double_divide(identity,identity),
    inference(symmetry,[status(thm)],[c70]) ).

cnf(c126,plain,
    double_divide(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)),inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)))) = double_divide(identity,identity),
    inference(transitivity,[status(thm)],[c124,c125]) ).

cnf(c127,plain,
    double_divide(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)),X) = double_divide(identity,identity),
    inference(transitivity,[status(thm)],[c122,c126]) ).

cnf(c128,plain,
    double_divide(multiply(double_divide(double_divide(identity,identity),double_divide(identity,X)),double_divide(identity,identity)),double_divide(identity,X)) = double_divide(identity,identity),
    inference(substitution,[status(thm)],[c127]) ).

cnf(c129,plain,
    double_divide(double_divide(identity,identity),double_divide(multiply(double_divide(double_divide(identity,identity),double_divide(identity,X)),double_divide(identity,identity)),double_divide(identity,X))) = double_divide(double_divide(identity,identity),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c128]) ).

cnf(c130,plain,
    double_divide(X,double_divide(double_divide(identity,identity),double_divide(multiply(double_divide(double_divide(identity,identity),double_divide(identity,X)),double_divide(identity,identity)),double_divide(identity,X)))) = double_divide(X,double_divide(double_divide(identity,identity),double_divide(identity,identity))),
    inference(congruence,[status(thm)],[c129]) ).

cnf(c131,plain,
    double_divide(double_divide(X,double_divide(double_divide(identity,identity),double_divide(multiply(double_divide(double_divide(identity,identity),double_divide(identity,X)),double_divide(identity,identity)),double_divide(identity,X)))),double_divide(identity,identity)) = double_divide(double_divide(X,double_divide(double_divide(identity,identity),double_divide(identity,identity))),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c130]) ).

cnf(c132,plain,
    double_divide(double_divide(X,double_divide(double_divide(identity,identity),double_divide(identity,identity))),double_divide(identity,identity)) = inverse(double_divide(X,double_divide(double_divide(identity,identity),double_divide(identity,identity)))),
    inference(substitution,[status(thm)],[c74]) ).

cnf(c133,plain,
    inverse(double_divide(X,double_divide(double_divide(identity,identity),double_divide(identity,identity)))) = multiply(double_divide(double_divide(identity,identity),double_divide(identity,identity)),X),
    inference(substitution,[status(thm)],[c82]) ).

cnf(c134,plain,
    multiply(double_divide(double_divide(identity,identity),double_divide(identity,identity)),X) = multiply(double_divide(identity,identity),X),
    inference(congruence,[status(thm)],[c60]) ).

cnf(c135,plain,
    multiply(double_divide(identity,identity),X) = multiply(identity,X),
    inference(congruence,[status(thm)],[c70]) ).

cnf(c136,plain,
    inverse(double_divide(X,identity)) = multiply(identity,X),
    inference(substitution,[status(thm)],[c82]) ).

cnf(c137,plain,
    multiply(identity,X) = inverse(double_divide(X,identity)),
    inference(symmetry,[status(thm)],[c136]) ).

cnf(c138,plain,
    inverse(X) = double_divide(X,identity),
    inference(substitution,[status(thm)],[c8]) ).

cnf(c139,plain,
    double_divide(X,identity) = inverse(X),
    inference(symmetry,[status(thm)],[c138]) ).

cnf(c140,plain,
    inverse(double_divide(X,identity)) = inverse(inverse(X)),
    inference(congruence,[status(thm)],[c139]) ).

cnf(c141,plain,
    multiply(identity,X) = inverse(inverse(X)),
    inference(transitivity,[status(thm)],[c137,c140]) ).

cnf(c142,plain,
    multiply(double_divide(identity,identity),X) = inverse(inverse(X)),
    inference(transitivity,[status(thm)],[c135,c141]) ).

cnf(c143,plain,
    multiply(double_divide(double_divide(identity,identity),double_divide(identity,identity)),X) = inverse(inverse(X)),
    inference(transitivity,[status(thm)],[c134,c142]) ).

cnf(c144,plain,
    inverse(double_divide(X,double_divide(double_divide(identity,identity),double_divide(identity,identity)))) = inverse(inverse(X)),
    inference(transitivity,[status(thm)],[c133,c143]) ).

cnf(c145,plain,
    double_divide(double_divide(X,double_divide(double_divide(identity,identity),double_divide(identity,identity))),double_divide(identity,identity)) = inverse(inverse(X)),
    inference(transitivity,[status(thm)],[c132,c144]) ).

cnf(c146,plain,
    double_divide(double_divide(X,double_divide(double_divide(identity,identity),double_divide(multiply(double_divide(double_divide(identity,identity),double_divide(identity,X)),double_divide(identity,identity)),double_divide(identity,X)))),double_divide(identity,identity)) = inverse(inverse(X)),
    inference(transitivity,[status(thm)],[c131,c145]) ).

cnf(c147,plain,
    multiply(double_divide(double_divide(identity,identity),double_divide(identity,X)),double_divide(identity,identity)) = inverse(inverse(X)),
    inference(transitivity,[status(thm)],[c120,c146]) ).

cnf(c148,plain,
    multiply(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),X)),double_divide(identity,identity)) = inverse(inverse(X)),
    inference(transitivity,[status(thm)],[c118,c147]) ).

cnf(c149,plain,
    inverse(multiply(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),X)),double_divide(identity,identity))) = inverse(inverse(inverse(X))),
    inference(congruence,[status(thm)],[c148]) ).

cnf(c150,plain,
    double_divide(double_divide(identity,identity),X) = inverse(inverse(inverse(X))),
    inference(transitivity,[status(thm)],[c115,c149]) ).

cnf(c151,plain,
    inverse(double_divide(double_divide(identity,identity),X)) = inverse(inverse(inverse(inverse(X)))),
    inference(congruence,[status(thm)],[c150]) ).

cnf(c152,plain,
    multiply(X,double_divide(identity,identity)) = inverse(inverse(inverse(inverse(X)))),
    inference(transitivity,[status(thm)],[c92,c151]) ).

cnf(c153,plain,
    multiply(inverse(inverse(inverse(double_divide(X,X2)))),double_divide(identity,identity)) = inverse(inverse(inverse(inverse(inverse(inverse(inverse(double_divide(X,X2)))))))),
    inference(substitution,[status(thm)],[c152]) ).

cnf(c154,plain,
    inverse(inverse(inverse(inverse(inverse(inverse(inverse(double_divide(X,X2)))))))) = multiply(inverse(inverse(inverse(double_divide(X,X2)))),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c153]) ).

cnf(c155,plain,
    double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),inverse(inverse(multiply(X2,double_divide(identity,identity)))))),double_divide(identity,identity)) = inverse(multiply(X2,double_divide(identity,identity))),
    inference(substitution,[status(thm)],[c31]) ).

cnf(c156,plain,
    inverse(multiply(X2,double_divide(identity,identity))) = double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),inverse(inverse(multiply(X2,double_divide(identity,identity)))))),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c155]) ).

cnf(c157,plain,
    inverse(double_divide(double_divide(identity,identity),X)) = multiply(X,double_divide(identity,identity)),
    inference(substitution,[status(thm)],[c82]) ).

cnf(c158,plain,
    multiply(X,double_divide(identity,identity)) = inverse(double_divide(double_divide(identity,identity),X)),
    inference(symmetry,[status(thm)],[c157]) ).

cnf(c159,plain,
    inverse(multiply(X,double_divide(identity,identity))) = inverse(inverse(double_divide(double_divide(identity,identity),X))),
    inference(congruence,[status(thm)],[c158]) ).

cnf(c160,plain,
    inverse(inverse(multiply(X,double_divide(identity,identity)))) = inverse(inverse(inverse(double_divide(double_divide(identity,identity),X)))),
    inference(congruence,[status(thm)],[c159]) ).

cnf(c161,plain,
    double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),X)) = inverse(inverse(inverse(double_divide(double_divide(identity,identity),X)))),
    inference(substitution,[status(thm)],[c150]) ).

cnf(c162,plain,
    inverse(inverse(inverse(double_divide(double_divide(identity,identity),X)))) = double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),X)),
    inference(symmetry,[status(thm)],[c161]) ).

cnf(c163,plain,
    inverse(double_divide(X2,X)) = multiply(X,X2),
    inference(substitution,[status(thm)],[c82]) ).

cnf(c164,plain,
    multiply(X2,X) = inverse(double_divide(X,X2)),
    inference(symmetry,[status(thm)],[c163]) ).

cnf(c165,plain,
    double_divide(double_divide(identity,X3),multiply(X2,X)) = double_divide(double_divide(identity,X3),inverse(double_divide(X,X2))),
    inference(congruence,[status(thm)],[c164]) ).

cnf(c166,plain,
    multiply(double_divide(double_divide(identity,X3),multiply(X2,X)),double_divide(X3,identity)) = multiply(double_divide(double_divide(identity,X3),inverse(double_divide(X,X2))),double_divide(X3,identity)),
    inference(congruence,[status(thm)],[c165]) ).

cnf(c167,plain,
    inverse(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),inverse(X)))) = multiply(double_divide(double_divide(identity,X2),inverse(X)),double_divide(X2,identity)),
    inference(substitution,[status(thm)],[c82]) ).

cnf(c168,plain,
    multiply(double_divide(double_divide(identity,X2),inverse(X)),double_divide(X2,identity)) = inverse(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),inverse(X)))),
    inference(symmetry,[status(thm)],[c167]) ).

cnf(c169,plain,
    inverse(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),inverse(X)))) = inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))),
    inference(congruence,[status(thm)],[c107]) ).

cnf(c170,plain,
    inverse(double_divide(double_divide(X2,identity),double_divide(double_divide(identity,X2),inverse(X)))) = X,
    inference(transitivity,[status(thm)],[c169,c113]) ).

cnf(c171,plain,
    multiply(double_divide(double_divide(identity,X2),inverse(X)),double_divide(X2,identity)) = X,
    inference(transitivity,[status(thm)],[c168,c170]) ).

cnf(c172,plain,
    multiply(double_divide(double_divide(identity,X3),inverse(double_divide(X,X2))),double_divide(X3,identity)) = double_divide(X,X2),
    inference(substitution,[status(thm)],[c171]) ).

cnf(c173,plain,
    multiply(double_divide(double_divide(identity,X3),multiply(X2,X)),double_divide(X3,identity)) = double_divide(X,X2),
    inference(transitivity,[status(thm)],[c166,c172]) ).

cnf(c174,plain,
    multiply(double_divide(double_divide(identity,identity),multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),X)),
    inference(substitution,[status(thm)],[c173]) ).

cnf(c175,plain,
    double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),X)) = multiply(double_divide(double_divide(identity,identity),multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c174]) ).

cnf(c176,plain,
    double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),inverse(X))) = multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)),
    inference(substitution,[status(thm)],[c107]) ).

cnf(c177,plain,
    multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)) = double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),inverse(X))),
    inference(symmetry,[status(thm)],[c176]) ).

cnf(c178,plain,
    double_divide(double_divide(identity,identity),multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))) = double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),inverse(X)))),
    inference(congruence,[status(thm)],[c177]) ).

cnf(c179,plain,
    multiply(double_divide(double_divide(identity,identity),multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))),double_divide(identity,identity)) = multiply(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),inverse(X)))),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c178]) ).

cnf(c180,plain,
    multiply(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),inverse(X)))),double_divide(identity,identity)) = inverse(inverse(double_divide(double_divide(identity,identity),inverse(X)))),
    inference(substitution,[status(thm)],[c148]) ).

cnf(c181,plain,
    inverse(double_divide(double_divide(identity,identity),inverse(X))) = multiply(inverse(X),double_divide(identity,identity)),
    inference(substitution,[status(thm)],[c82]) ).

cnf(c182,plain,
    inverse(inverse(double_divide(double_divide(identity,identity),inverse(X)))) = inverse(multiply(inverse(X),double_divide(identity,identity))),
    inference(congruence,[status(thm)],[c181]) ).

cnf(c183,plain,
    multiply(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),inverse(X)))),double_divide(identity,identity)) = inverse(multiply(inverse(X),double_divide(identity,identity))),
    inference(transitivity,[status(thm)],[c180,c182]) ).

cnf(c184,plain,
    multiply(double_divide(double_divide(identity,identity),multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))),double_divide(identity,identity)) = inverse(multiply(inverse(X),double_divide(identity,identity))),
    inference(transitivity,[status(thm)],[c179,c183]) ).

cnf(c185,plain,
    double_divide(double_divide(identity,identity),double_divide(double_divide(identity,identity),X)) = inverse(multiply(inverse(X),double_divide(identity,identity))),
    inference(transitivity,[status(thm)],[c175,c184]) ).

cnf(c186,plain,
    inverse(inverse(inverse(double_divide(double_divide(identity,identity),X)))) = inverse(multiply(inverse(X),double_divide(identity,identity))),
    inference(transitivity,[status(thm)],[c162,c185]) ).

cnf(c187,plain,
    inverse(inverse(multiply(X,double_divide(identity,identity)))) = inverse(multiply(inverse(X),double_divide(identity,identity))),
    inference(transitivity,[status(thm)],[c160,c186]) ).

cnf(c188,plain,
    double_divide(double_divide(identity,X),inverse(inverse(multiply(X2,double_divide(identity,identity))))) = double_divide(double_divide(identity,X),inverse(multiply(inverse(X2),double_divide(identity,identity)))),
    inference(congruence,[status(thm)],[c187]) ).

cnf(c189,plain,
    double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),inverse(inverse(multiply(X2,double_divide(identity,identity)))))) = double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),inverse(multiply(inverse(X2),double_divide(identity,identity))))),
    inference(congruence,[status(thm)],[c188]) ).

cnf(c190,plain,
    double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),inverse(inverse(multiply(X2,double_divide(identity,identity)))))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),inverse(multiply(inverse(X2),double_divide(identity,identity))))),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c189]) ).

cnf(c191,plain,
    double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),inverse(multiply(inverse(X2),double_divide(identity,identity))))),double_divide(identity,identity)) = multiply(inverse(X2),double_divide(identity,identity)),
    inference(substitution,[status(thm)],[c31]) ).

cnf(c192,plain,
    double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),inverse(inverse(multiply(X2,double_divide(identity,identity)))))),double_divide(identity,identity)) = multiply(inverse(X2),double_divide(identity,identity)),
    inference(transitivity,[status(thm)],[c190,c191]) ).

cnf(c193,plain,
    inverse(multiply(X,double_divide(identity,identity))) = multiply(inverse(X),double_divide(identity,identity)),
    inference(transitivity,[status(thm)],[c156,c192]) ).

cnf(c194,plain,
    inverse(multiply(inverse(inverse(double_divide(X,X2))),double_divide(identity,identity))) = multiply(inverse(inverse(inverse(double_divide(X,X2)))),double_divide(identity,identity)),
    inference(substitution,[status(thm)],[c193]) ).

cnf(c195,plain,
    multiply(inverse(inverse(inverse(double_divide(X,X2)))),double_divide(identity,identity)) = inverse(multiply(inverse(inverse(double_divide(X,X2))),double_divide(identity,identity))),
    inference(symmetry,[status(thm)],[c194]) ).

cnf(c196,plain,
    inverse(inverse(multiply(inverse(double_divide(X,X2)),double_divide(identity,identity)))) = inverse(multiply(inverse(inverse(double_divide(X,X2))),double_divide(identity,identity))),
    inference(substitution,[status(thm)],[c187]) ).

cnf(c197,plain,
    inverse(multiply(inverse(inverse(double_divide(X,X2))),double_divide(identity,identity))) = inverse(inverse(multiply(inverse(double_divide(X,X2)),double_divide(identity,identity)))),
    inference(symmetry,[status(thm)],[c196]) ).

cnf(c198,plain,
    inverse(inverse(multiply(double_divide(X,X2),double_divide(identity,identity)))) = inverse(multiply(inverse(double_divide(X,X2)),double_divide(identity,identity))),
    inference(substitution,[status(thm)],[c187]) ).

cnf(c199,plain,
    inverse(multiply(inverse(double_divide(X,X2)),double_divide(identity,identity))) = inverse(inverse(multiply(double_divide(X,X2),double_divide(identity,identity)))),
    inference(symmetry,[status(thm)],[c198]) ).

cnf(c200,plain,
    inverse(inverse(multiply(inverse(double_divide(X,X2)),double_divide(identity,identity)))) = inverse(inverse(inverse(multiply(double_divide(X,X2),double_divide(identity,identity))))),
    inference(congruence,[status(thm)],[c199]) ).

cnf(c201,plain,
    inverse(double_divide(double_divide(identity,identity),double_divide(X,X2))) = multiply(double_divide(X,X2),double_divide(identity,identity)),
    inference(substitution,[status(thm)],[c82]) ).

cnf(c202,plain,
    multiply(double_divide(X,X2),double_divide(identity,identity)) = inverse(double_divide(double_divide(identity,identity),double_divide(X,X2))),
    inference(symmetry,[status(thm)],[c201]) ).

cnf(c203,plain,
    inverse(multiply(double_divide(X,X2),double_divide(identity,identity))) = inverse(inverse(double_divide(double_divide(identity,identity),double_divide(X,X2)))),
    inference(congruence,[status(thm)],[c202]) ).

cnf(c204,plain,
    inverse(inverse(multiply(double_divide(X,X2),double_divide(identity,identity)))) = inverse(inverse(inverse(double_divide(double_divide(identity,identity),double_divide(X,X2))))),
    inference(congruence,[status(thm)],[c203]) ).

cnf(c205,plain,
    inverse(inverse(inverse(multiply(double_divide(X,X2),double_divide(identity,identity))))) = inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),double_divide(X,X2)))))),
    inference(congruence,[status(thm)],[c204]) ).

cnf(c206,plain,
    multiply(double_divide(double_divide(identity,identity),double_divide(X,X2)),double_divide(identity,identity)) = inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),double_divide(X,X2)))))),
    inference(substitution,[status(thm)],[c152]) ).

cnf(c207,plain,
    inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),double_divide(X,X2)))))) = multiply(double_divide(double_divide(identity,identity),double_divide(X,X2)),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c206]) ).

cnf(c208,plain,
    double_divide(double_divide(X2,double_divide(double_divide(identity,X),double_divide(multiply(double_divide(double_divide(identity,identity),double_divide(X,X2)),double_divide(identity,identity)),double_divide(X,X2)))),double_divide(identity,identity)) = multiply(double_divide(double_divide(identity,identity),double_divide(X,X2)),double_divide(identity,identity)),
    inference(substitution,[status(thm)],[c5]) ).

cnf(c209,plain,
    multiply(double_divide(double_divide(identity,identity),double_divide(X,X2)),double_divide(identity,identity)) = double_divide(double_divide(X2,double_divide(double_divide(identity,X),double_divide(multiply(double_divide(double_divide(identity,identity),double_divide(X,X2)),double_divide(identity,identity)),double_divide(X,X2)))),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c208]) ).

cnf(c210,plain,
    double_divide(multiply(double_divide(double_divide(identity,identity),double_divide(X,X2)),double_divide(identity,identity)),double_divide(X,X2)) = double_divide(identity,identity),
    inference(substitution,[status(thm)],[c127]) ).

cnf(c211,plain,
    double_divide(double_divide(identity,X),double_divide(multiply(double_divide(double_divide(identity,identity),double_divide(X,X2)),double_divide(identity,identity)),double_divide(X,X2))) = double_divide(double_divide(identity,X),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c210]) ).

cnf(c212,plain,
    double_divide(X2,double_divide(double_divide(identity,X),double_divide(multiply(double_divide(double_divide(identity,identity),double_divide(X,X2)),double_divide(identity,identity)),double_divide(X,X2)))) = double_divide(X2,double_divide(double_divide(identity,X),double_divide(identity,identity))),
    inference(congruence,[status(thm)],[c211]) ).

cnf(c213,plain,
    double_divide(double_divide(X2,double_divide(double_divide(identity,X),double_divide(multiply(double_divide(double_divide(identity,identity),double_divide(X,X2)),double_divide(identity,identity)),double_divide(X,X2)))),double_divide(identity,identity)) = double_divide(double_divide(X2,double_divide(double_divide(identity,X),double_divide(identity,identity))),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c212]) ).

cnf(c214,plain,
    double_divide(double_divide(X2,double_divide(double_divide(identity,X),double_divide(identity,identity))),double_divide(identity,identity)) = inverse(double_divide(X2,double_divide(double_divide(identity,X),double_divide(identity,identity)))),
    inference(substitution,[status(thm)],[c74]) ).

cnf(c215,plain,
    inverse(double_divide(X2,double_divide(double_divide(identity,X),double_divide(identity,identity)))) = multiply(double_divide(double_divide(identity,X),double_divide(identity,identity)),X2),
    inference(substitution,[status(thm)],[c82]) ).

cnf(c216,plain,
    double_divide(double_divide(identity,X),double_divide(identity,identity)) = inverse(double_divide(identity,X)),
    inference(substitution,[status(thm)],[c74]) ).

cnf(c217,plain,
    multiply(double_divide(double_divide(identity,X),double_divide(identity,identity)),X2) = multiply(inverse(double_divide(identity,X)),X2),
    inference(congruence,[status(thm)],[c216]) ).

cnf(c218,plain,
    inverse(double_divide(identity,X)) = multiply(X,identity),
    inference(substitution,[status(thm)],[c82]) ).

cnf(c219,plain,
    multiply(inverse(double_divide(identity,X)),X2) = multiply(multiply(X,identity),X2),
    inference(congruence,[status(thm)],[c218]) ).

cnf(c220,plain,
    identity = double_divide(identity,identity),
    inference(symmetry,[status(thm)],[c70]) ).

cnf(c221,plain,
    multiply(X,identity) = multiply(X,double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c220]) ).

cnf(c222,plain,
    multiply(multiply(X,identity),X2) = multiply(multiply(X,double_divide(identity,identity)),X2),
    inference(congruence,[status(thm)],[c221]) ).

cnf(c223,plain,
    multiply(multiply(X,double_divide(identity,identity)),X2) = multiply(inverse(inverse(inverse(inverse(X)))),X2),
    inference(congruence,[status(thm)],[c152]) ).

cnf(c224,plain,
    multiply(multiply(X,identity),X2) = multiply(inverse(inverse(inverse(inverse(X)))),X2),
    inference(transitivity,[status(thm)],[c222,c223]) ).

cnf(c225,plain,
    multiply(inverse(double_divide(identity,X)),X2) = multiply(inverse(inverse(inverse(inverse(X)))),X2),
    inference(transitivity,[status(thm)],[c219,c224]) ).

cnf(c226,plain,
    multiply(double_divide(double_divide(identity,X),double_divide(identity,identity)),X2) = multiply(inverse(inverse(inverse(inverse(X)))),X2),
    inference(transitivity,[status(thm)],[c217,c225]) ).

cnf(c227,plain,
    inverse(double_divide(X2,double_divide(double_divide(identity,X),double_divide(identity,identity)))) = multiply(inverse(inverse(inverse(inverse(X)))),X2),
    inference(transitivity,[status(thm)],[c215,c226]) ).

cnf(c228,plain,
    double_divide(double_divide(X2,double_divide(double_divide(identity,X),double_divide(identity,identity))),double_divide(identity,identity)) = multiply(inverse(inverse(inverse(inverse(X)))),X2),
    inference(transitivity,[status(thm)],[c214,c227]) ).

cnf(c229,plain,
    double_divide(double_divide(X2,double_divide(double_divide(identity,X),double_divide(multiply(double_divide(double_divide(identity,identity),double_divide(X,X2)),double_divide(identity,identity)),double_divide(X,X2)))),double_divide(identity,identity)) = multiply(inverse(inverse(inverse(inverse(X)))),X2),
    inference(transitivity,[status(thm)],[c213,c228]) ).

cnf(c230,plain,
    multiply(double_divide(double_divide(identity,identity),double_divide(X,X2)),double_divide(identity,identity)) = multiply(inverse(inverse(inverse(inverse(X)))),X2),
    inference(transitivity,[status(thm)],[c209,c229]) ).

cnf(c231,plain,
    inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),double_divide(X,X2)))))) = multiply(inverse(inverse(inverse(inverse(X)))),X2),
    inference(transitivity,[status(thm)],[c207,c230]) ).

cnf(c232,plain,
    inverse(inverse(inverse(multiply(double_divide(X,X2),double_divide(identity,identity))))) = multiply(inverse(inverse(inverse(inverse(X)))),X2),
    inference(transitivity,[status(thm)],[c205,c231]) ).

cnf(c233,plain,
    inverse(inverse(multiply(inverse(double_divide(X,X2)),double_divide(identity,identity)))) = multiply(inverse(inverse(inverse(inverse(X)))),X2),
    inference(transitivity,[status(thm)],[c200,c232]) ).

cnf(c234,plain,
    inverse(multiply(inverse(inverse(double_divide(X,X2))),double_divide(identity,identity))) = multiply(inverse(inverse(inverse(inverse(X)))),X2),
    inference(transitivity,[status(thm)],[c197,c233]) ).

cnf(c235,plain,
    multiply(inverse(inverse(inverse(double_divide(X,X2)))),double_divide(identity,identity)) = multiply(inverse(inverse(inverse(inverse(X)))),X2),
    inference(transitivity,[status(thm)],[c195,c234]) ).

cnf(c236,plain,
    inverse(inverse(inverse(inverse(inverse(inverse(inverse(double_divide(X,X2)))))))) = multiply(inverse(inverse(inverse(inverse(X)))),X2),
    inference(transitivity,[status(thm)],[c154,c235]) ).

cnf(c237,plain,
    inverse(inverse(inverse(inverse(inverse(inverse(multiply(X2,X))))))) = multiply(inverse(inverse(inverse(inverse(X)))),X2),
    inference(transitivity,[status(thm)],[c90,c236]) ).

cnf(c238,plain,
    inverse(inverse(inverse(inverse(inverse(inverse(multiply(identity,X))))))) = multiply(inverse(inverse(inverse(inverse(X)))),identity),
    inference(substitution,[status(thm)],[c237]) ).

cnf(c239,plain,
    inverse(inverse(X)) = multiply(identity,X),
    inference(symmetry,[status(thm)],[c141]) ).

cnf(c240,plain,
    inverse(inverse(inverse(X))) = inverse(multiply(identity,X)),
    inference(congruence,[status(thm)],[c239]) ).

cnf(c241,plain,
    inverse(inverse(inverse(inverse(X)))) = inverse(inverse(multiply(identity,X))),
    inference(congruence,[status(thm)],[c240]) ).

cnf(c242,plain,
    multiply(inverse(inverse(inverse(inverse(X)))),identity) = multiply(inverse(inverse(multiply(identity,X))),identity),
    inference(congruence,[status(thm)],[c241]) ).

cnf(c243,plain,
    identity = double_divide(identity,identity),
    inference(symmetry,[status(thm)],[c70]) ).

cnf(c244,plain,
    multiply(inverse(inverse(multiply(identity,X))),identity) = multiply(inverse(inverse(multiply(identity,X))),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c243]) ).

cnf(c245,plain,
    inverse(multiply(identity,X)) = inverse(inverse(inverse(X))),
    inference(congruence,[status(thm)],[c141]) ).

cnf(c246,plain,
    inverse(inverse(multiply(identity,X))) = inverse(inverse(inverse(inverse(X)))),
    inference(congruence,[status(thm)],[c245]) ).

cnf(c247,plain,
    multiply(inverse(inverse(multiply(identity,X))),double_divide(identity,identity)) = multiply(inverse(inverse(inverse(inverse(X)))),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c246]) ).

cnf(c248,plain,
    double_divide(double_divide(identity,identity),inverse(X)) = inverse(inverse(inverse(inverse(X)))),
    inference(substitution,[status(thm)],[c150]) ).

cnf(c249,plain,
    inverse(inverse(inverse(inverse(X)))) = double_divide(double_divide(identity,identity),inverse(X)),
    inference(symmetry,[status(thm)],[c248]) ).

cnf(c250,plain,
    multiply(inverse(inverse(inverse(inverse(X)))),double_divide(identity,identity)) = multiply(double_divide(double_divide(identity,identity),inverse(X)),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c249]) ).

cnf(c251,plain,
    multiply(double_divide(double_divide(identity,identity),inverse(X)),double_divide(identity,identity)) = X,
    inference(substitution,[status(thm)],[c171]) ).

cnf(c252,plain,
    multiply(inverse(inverse(inverse(inverse(X)))),double_divide(identity,identity)) = X,
    inference(transitivity,[status(thm)],[c250,c251]) ).

cnf(c253,plain,
    multiply(inverse(inverse(multiply(identity,X))),double_divide(identity,identity)) = X,
    inference(transitivity,[status(thm)],[c247,c252]) ).

cnf(c254,plain,
    multiply(inverse(inverse(multiply(identity,X))),identity) = X,
    inference(transitivity,[status(thm)],[c244,c253]) ).

cnf(c255,plain,
    multiply(inverse(inverse(inverse(inverse(X)))),identity) = X,
    inference(transitivity,[status(thm)],[c242,c254]) ).

cnf(c256,plain,
    inverse(inverse(inverse(inverse(inverse(inverse(multiply(identity,X))))))) = X,
    inference(transitivity,[status(thm)],[c238,c255]) ).

cnf(c257,plain,
    X = inverse(inverse(inverse(inverse(inverse(inverse(multiply(identity,X))))))),
    inference(symmetry,[status(thm)],[c256]) ).

cnf(c258,plain,
    double_divide(X2,double_divide(X,double_divide(identity,identity))) = double_divide(inverse(inverse(inverse(inverse(inverse(inverse(multiply(identity,X2))))))),double_divide(X,double_divide(identity,identity))),
    inference(congruence,[status(thm)],[c257]) ).

cnf(c259,plain,
    multiply(double_divide(X2,double_divide(X,double_divide(identity,identity))),X2) = multiply(double_divide(inverse(inverse(inverse(inverse(inverse(inverse(multiply(identity,X2))))))),double_divide(X,double_divide(identity,identity))),X2),
    inference(congruence,[status(thm)],[c258]) ).

cnf(c260,plain,
    double_divide(double_divide(identity,identity),inverse(inverse(inverse(multiply(identity,X))))) = inverse(inverse(inverse(inverse(inverse(inverse(multiply(identity,X))))))),
    inference(substitution,[status(thm)],[c150]) ).

cnf(c261,plain,
    inverse(inverse(inverse(inverse(inverse(inverse(multiply(identity,X))))))) = double_divide(double_divide(identity,identity),inverse(inverse(inverse(multiply(identity,X))))),
    inference(symmetry,[status(thm)],[c260]) ).

cnf(c262,plain,
    double_divide(inverse(inverse(inverse(inverse(inverse(inverse(multiply(identity,X2))))))),double_divide(X,double_divide(identity,identity))) = double_divide(double_divide(double_divide(identity,identity),inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity))),
    inference(congruence,[status(thm)],[c261]) ).

cnf(c263,plain,
    multiply(double_divide(inverse(inverse(inverse(inverse(inverse(inverse(multiply(identity,X2))))))),double_divide(X,double_divide(identity,identity))),X2) = multiply(double_divide(double_divide(double_divide(identity,identity),inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity))),X2),
    inference(congruence,[status(thm)],[c262]) ).

cnf(c264,plain,
    double_divide(double_divide(identity,identity),inverse(inverse(inverse(multiply(identity,X))))) = double_divide(identity,inverse(inverse(inverse(multiply(identity,X))))),
    inference(congruence,[status(thm)],[c70]) ).

cnf(c265,plain,
    double_divide(double_divide(double_divide(identity,identity),inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity))) = double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity))),
    inference(congruence,[status(thm)],[c264]) ).

cnf(c266,plain,
    multiply(double_divide(double_divide(double_divide(identity,identity),inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity))),X2) = multiply(double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity))),X2),
    inference(congruence,[status(thm)],[c265]) ).

cnf(c267,plain,
    inverse(double_divide(X2,double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity))))) = multiply(double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity))),X2),
    inference(substitution,[status(thm)],[c82]) ).

cnf(c268,plain,
    multiply(double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity))),X2) = inverse(double_divide(X2,double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity))))),
    inference(symmetry,[status(thm)],[c267]) ).

cnf(c269,plain,
    double_divide(double_divide(X2,double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity)))),double_divide(identity,identity)) = inverse(double_divide(X2,double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity))))),
    inference(substitution,[status(thm)],[c74]) ).

cnf(c270,plain,
    inverse(double_divide(X2,double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity))))) = double_divide(double_divide(X2,double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity)))),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c269]) ).

cnf(c271,plain,
    X = inverse(inverse(inverse(inverse(inverse(inverse(multiply(identity,X))))))),
    inference(symmetry,[status(thm)],[c256]) ).

cnf(c272,plain,
    double_divide(inverse(inverse(inverse(multiply(identity,X)))),X) = double_divide(inverse(inverse(inverse(multiply(identity,X)))),inverse(inverse(inverse(inverse(inverse(inverse(multiply(identity,X)))))))),
    inference(congruence,[status(thm)],[c271]) ).

cnf(c273,plain,
    double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),double_divide(identity,identity))),double_divide(identity,identity)) = identity,
    inference(substitution,[status(thm)],[c32]) ).

cnf(c274,plain,
    identity = double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),double_divide(identity,identity))),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c273]) ).

cnf(c275,plain,
    inverse(double_divide(identity,identity)) = inverse(identity),
    inference(congruence,[status(thm)],[c70]) ).

cnf(c276,plain,
    inverse(identity) = double_divide(identity,identity),
    inference(substitution,[status(thm)],[c8]) ).

cnf(c277,plain,
    inverse(double_divide(identity,identity)) = double_divide(identity,identity),
    inference(transitivity,[status(thm)],[c275,c276]) ).

cnf(c278,plain,
    double_divide(identity,identity) = inverse(double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c277]) ).

cnf(c279,plain,
    double_divide(identity,identity) = inverse(double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c277]) ).

cnf(c280,plain,
    inverse(double_divide(identity,identity)) = inverse(inverse(double_divide(identity,identity))),
    inference(congruence,[status(thm)],[c279]) ).

cnf(c281,plain,
    double_divide(identity,identity) = inverse(double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c277]) ).

cnf(c282,plain,
    inverse(double_divide(identity,identity)) = inverse(inverse(double_divide(identity,identity))),
    inference(congruence,[status(thm)],[c281]) ).

cnf(c283,plain,
    inverse(inverse(double_divide(identity,identity))) = inverse(inverse(inverse(double_divide(identity,identity)))),
    inference(congruence,[status(thm)],[c282]) ).

cnf(c284,plain,
    double_divide(identity,identity) = inverse(double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c277]) ).

cnf(c285,plain,
    inverse(double_divide(identity,identity)) = inverse(inverse(double_divide(identity,identity))),
    inference(congruence,[status(thm)],[c284]) ).

cnf(c286,plain,
    inverse(inverse(double_divide(identity,identity))) = inverse(inverse(inverse(double_divide(identity,identity)))),
    inference(congruence,[status(thm)],[c285]) ).

cnf(c287,plain,
    inverse(inverse(inverse(double_divide(identity,identity)))) = inverse(inverse(inverse(inverse(double_divide(identity,identity))))),
    inference(congruence,[status(thm)],[c286]) ).

cnf(c288,plain,
    double_divide(identity,identity) = inverse(double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c277]) ).

cnf(c289,plain,
    inverse(double_divide(identity,identity)) = inverse(inverse(double_divide(identity,identity))),
    inference(congruence,[status(thm)],[c288]) ).

cnf(c290,plain,
    inverse(inverse(double_divide(identity,identity))) = inverse(inverse(inverse(double_divide(identity,identity)))),
    inference(congruence,[status(thm)],[c289]) ).

cnf(c291,plain,
    inverse(inverse(inverse(double_divide(identity,identity)))) = inverse(inverse(inverse(inverse(double_divide(identity,identity))))),
    inference(congruence,[status(thm)],[c290]) ).

cnf(c292,plain,
    inverse(inverse(inverse(inverse(double_divide(identity,identity))))) = inverse(inverse(inverse(inverse(inverse(double_divide(identity,identity)))))),
    inference(congruence,[status(thm)],[c291]) ).

cnf(c293,plain,
    double_divide(identity,identity) = inverse(double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c277]) ).

cnf(c294,plain,
    inverse(double_divide(identity,identity)) = inverse(inverse(double_divide(identity,identity))),
    inference(congruence,[status(thm)],[c293]) ).

cnf(c295,plain,
    inverse(inverse(double_divide(identity,identity))) = inverse(inverse(inverse(double_divide(identity,identity)))),
    inference(congruence,[status(thm)],[c294]) ).

cnf(c296,plain,
    inverse(inverse(inverse(double_divide(identity,identity)))) = inverse(inverse(inverse(inverse(double_divide(identity,identity))))),
    inference(congruence,[status(thm)],[c295]) ).

cnf(c297,plain,
    inverse(inverse(inverse(inverse(double_divide(identity,identity))))) = inverse(inverse(inverse(inverse(inverse(double_divide(identity,identity)))))),
    inference(congruence,[status(thm)],[c296]) ).

cnf(c298,plain,
    inverse(inverse(inverse(inverse(inverse(double_divide(identity,identity)))))) = inverse(inverse(inverse(inverse(inverse(inverse(double_divide(identity,identity))))))),
    inference(congruence,[status(thm)],[c297]) ).

cnf(c299,plain,
    X = inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))),
    inference(symmetry,[status(thm)],[c113]) ).

cnf(c300,plain,
    multiply(X,multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))) = multiply(inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))),multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))),
    inference(congruence,[status(thm)],[c299]) ).

cnf(c301,plain,
    inverse(identity) = double_divide(identity,identity),
    inference(substitution,[status(thm)],[c8]) ).

cnf(c302,plain,
    double_divide(identity,identity) = inverse(identity),
    inference(symmetry,[status(thm)],[c301]) ).

cnf(c303,plain,
    identity = double_divide(X,inverse(X)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c304,plain,
    inverse(identity) = inverse(double_divide(X,inverse(X))),
    inference(congruence,[status(thm)],[c303]) ).

cnf(c305,plain,
    inverse(double_divide(X,inverse(X))) = multiply(inverse(X),X),
    inference(substitution,[status(thm)],[c82]) ).

cnf(c306,plain,
    inverse(identity) = multiply(inverse(X),X),
    inference(transitivity,[status(thm)],[c304,c305]) ).

cnf(c307,plain,
    double_divide(identity,identity) = multiply(inverse(X),X),
    inference(transitivity,[status(thm)],[c302,c306]) ).

cnf(c308,plain,
    double_divide(identity,identity) = multiply(inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))),multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))),
    inference(substitution,[status(thm)],[c307]) ).

cnf(c309,plain,
    multiply(inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))),multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))) = double_divide(identity,identity),
    inference(symmetry,[status(thm)],[c308]) ).

cnf(c310,plain,
    multiply(X,multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))) = double_divide(identity,identity),
    inference(transitivity,[status(thm)],[c300,c309]) ).

cnf(c311,plain,
    double_divide(identity,identity) = multiply(X,multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))),
    inference(symmetry,[status(thm)],[c310]) ).

cnf(c312,plain,
    inverse(double_divide(identity,identity)) = inverse(multiply(X,multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)))),
    inference(congruence,[status(thm)],[c311]) ).

cnf(c313,plain,
    inverse(inverse(double_divide(identity,identity))) = inverse(inverse(multiply(X,multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))))),
    inference(congruence,[status(thm)],[c312]) ).

cnf(c314,plain,
    inverse(inverse(inverse(double_divide(identity,identity)))) = inverse(inverse(inverse(multiply(X,multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)))))),
    inference(congruence,[status(thm)],[c313]) ).

cnf(c315,plain,
    inverse(inverse(inverse(inverse(double_divide(identity,identity))))) = inverse(inverse(inverse(inverse(multiply(X,multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))))))),
    inference(congruence,[status(thm)],[c314]) ).

cnf(c316,plain,
    inverse(inverse(inverse(inverse(inverse(double_divide(identity,identity)))))) = inverse(inverse(inverse(inverse(inverse(multiply(X,multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)))))))),
    inference(congruence,[status(thm)],[c315]) ).

cnf(c317,plain,
    inverse(inverse(inverse(inverse(inverse(inverse(double_divide(identity,identity))))))) = inverse(inverse(inverse(inverse(inverse(inverse(multiply(X,multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))))))))),
    inference(congruence,[status(thm)],[c316]) ).

cnf(c318,plain,
    inverse(inverse(inverse(inverse(inverse(inverse(multiply(X,multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))))))))) = multiply(inverse(inverse(inverse(inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)))))),X),
    inference(substitution,[status(thm)],[c237]) ).

cnf(c319,plain,
    inverse(inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)))) = inverse(multiply(inverse(double_divide(double_divide(identity,identity),X)),double_divide(identity,identity))),
    inference(substitution,[status(thm)],[c187]) ).

cnf(c320,plain,
    inverse(inverse(inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))))) = inverse(inverse(multiply(inverse(double_divide(double_divide(identity,identity),X)),double_divide(identity,identity)))),
    inference(congruence,[status(thm)],[c319]) ).

cnf(c321,plain,
    inverse(inverse(inverse(inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)))))) = inverse(inverse(inverse(multiply(inverse(double_divide(double_divide(identity,identity),X)),double_divide(identity,identity))))),
    inference(congruence,[status(thm)],[c320]) ).

cnf(c322,plain,
    multiply(inverse(inverse(inverse(inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)))))),X) = multiply(inverse(inverse(inverse(multiply(inverse(double_divide(double_divide(identity,identity),X)),double_divide(identity,identity))))),X),
    inference(congruence,[status(thm)],[c321]) ).

cnf(c323,plain,
    inverse(inverse(multiply(inverse(double_divide(double_divide(identity,identity),X)),double_divide(identity,identity)))) = inverse(multiply(inverse(inverse(double_divide(double_divide(identity,identity),X))),double_divide(identity,identity))),
    inference(substitution,[status(thm)],[c187]) ).

cnf(c324,plain,
    inverse(inverse(inverse(multiply(inverse(double_divide(double_divide(identity,identity),X)),double_divide(identity,identity))))) = inverse(inverse(multiply(inverse(inverse(double_divide(double_divide(identity,identity),X))),double_divide(identity,identity)))),
    inference(congruence,[status(thm)],[c323]) ).

cnf(c325,plain,
    multiply(inverse(inverse(inverse(multiply(inverse(double_divide(double_divide(identity,identity),X)),double_divide(identity,identity))))),X) = multiply(inverse(inverse(multiply(inverse(inverse(double_divide(double_divide(identity,identity),X))),double_divide(identity,identity)))),X),
    inference(congruence,[status(thm)],[c324]) ).

cnf(c326,plain,
    inverse(inverse(multiply(inverse(inverse(double_divide(double_divide(identity,identity),X))),double_divide(identity,identity)))) = inverse(multiply(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X)))),double_divide(identity,identity))),
    inference(substitution,[status(thm)],[c187]) ).

cnf(c327,plain,
    multiply(inverse(inverse(multiply(inverse(inverse(double_divide(double_divide(identity,identity),X))),double_divide(identity,identity)))),X) = multiply(inverse(multiply(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X)))),double_divide(identity,identity))),X),
    inference(congruence,[status(thm)],[c326]) ).

cnf(c328,plain,
    inverse(multiply(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X)))),double_divide(identity,identity))) = multiply(inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X))))),double_divide(identity,identity)),
    inference(substitution,[status(thm)],[c193]) ).

cnf(c329,plain,
    multiply(inverse(multiply(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X)))),double_divide(identity,identity))),X) = multiply(multiply(inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X))))),double_divide(identity,identity)),X),
    inference(congruence,[status(thm)],[c328]) ).

cnf(c330,plain,
    multiply(inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X))))),double_divide(identity,identity)) = inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X))))))))),
    inference(substitution,[status(thm)],[c152]) ).

cnf(c331,plain,
    multiply(multiply(inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X))))),double_divide(identity,identity)),X) = multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X))))))))),X),
    inference(congruence,[status(thm)],[c330]) ).

cnf(c332,plain,
    multiply(inverse(inverse(inverse(inverse(X)))),double_divide(identity,identity)) = inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(X)))))))),
    inference(substitution,[status(thm)],[c152]) ).

cnf(c333,plain,
    inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(X)))))))) = multiply(inverse(inverse(inverse(inverse(X)))),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c332]) ).

cnf(c334,plain,
    inverse(multiply(inverse(inverse(inverse(X))),double_divide(identity,identity))) = multiply(inverse(inverse(inverse(inverse(X)))),double_divide(identity,identity)),
    inference(substitution,[status(thm)],[c193]) ).

cnf(c335,plain,
    multiply(inverse(inverse(inverse(inverse(X)))),double_divide(identity,identity)) = inverse(multiply(inverse(inverse(inverse(X))),double_divide(identity,identity))),
    inference(symmetry,[status(thm)],[c334]) ).

cnf(c336,plain,
    inverse(inverse(multiply(inverse(inverse(X)),double_divide(identity,identity)))) = inverse(multiply(inverse(inverse(inverse(X))),double_divide(identity,identity))),
    inference(substitution,[status(thm)],[c187]) ).

cnf(c337,plain,
    inverse(multiply(inverse(inverse(inverse(X))),double_divide(identity,identity))) = inverse(inverse(multiply(inverse(inverse(X)),double_divide(identity,identity)))),
    inference(symmetry,[status(thm)],[c336]) ).

cnf(c338,plain,
    inverse(inverse(multiply(inverse(X),double_divide(identity,identity)))) = inverse(multiply(inverse(inverse(X)),double_divide(identity,identity))),
    inference(substitution,[status(thm)],[c187]) ).

cnf(c339,plain,
    inverse(multiply(inverse(inverse(X)),double_divide(identity,identity))) = inverse(inverse(multiply(inverse(X),double_divide(identity,identity)))),
    inference(symmetry,[status(thm)],[c338]) ).

cnf(c340,plain,
    inverse(inverse(multiply(inverse(inverse(X)),double_divide(identity,identity)))) = inverse(inverse(inverse(multiply(inverse(X),double_divide(identity,identity))))),
    inference(congruence,[status(thm)],[c339]) ).

cnf(c341,plain,
    inverse(multiply(inverse(X),double_divide(identity,identity))) = inverse(inverse(multiply(X,double_divide(identity,identity)))),
    inference(symmetry,[status(thm)],[c187]) ).

cnf(c342,plain,
    inverse(inverse(multiply(inverse(X),double_divide(identity,identity)))) = inverse(inverse(inverse(multiply(X,double_divide(identity,identity))))),
    inference(congruence,[status(thm)],[c341]) ).

cnf(c343,plain,
    inverse(inverse(inverse(multiply(inverse(X),double_divide(identity,identity))))) = inverse(inverse(inverse(inverse(multiply(X,double_divide(identity,identity)))))),
    inference(congruence,[status(thm)],[c342]) ).

cnf(c344,plain,
    inverse(double_divide(double_divide(identity,identity),X)) = multiply(X,double_divide(identity,identity)),
    inference(substitution,[status(thm)],[c82]) ).

cnf(c345,plain,
    multiply(X,double_divide(identity,identity)) = inverse(double_divide(double_divide(identity,identity),X)),
    inference(symmetry,[status(thm)],[c344]) ).

cnf(c346,plain,
    inverse(multiply(X,double_divide(identity,identity))) = inverse(inverse(double_divide(double_divide(identity,identity),X))),
    inference(congruence,[status(thm)],[c345]) ).

cnf(c347,plain,
    inverse(inverse(multiply(X,double_divide(identity,identity)))) = inverse(inverse(inverse(double_divide(double_divide(identity,identity),X)))),
    inference(congruence,[status(thm)],[c346]) ).

cnf(c348,plain,
    inverse(inverse(inverse(multiply(X,double_divide(identity,identity))))) = inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X))))),
    inference(congruence,[status(thm)],[c347]) ).

cnf(c349,plain,
    inverse(inverse(inverse(inverse(multiply(X,double_divide(identity,identity)))))) = inverse(inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X)))))),
    inference(congruence,[status(thm)],[c348]) ).

cnf(c350,plain,
    multiply(inverse(double_divide(double_divide(identity,identity),X)),double_divide(identity,identity)) = inverse(inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X)))))),
    inference(substitution,[status(thm)],[c152]) ).

cnf(c351,plain,
    inverse(inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X)))))) = multiply(inverse(double_divide(double_divide(identity,identity),X)),double_divide(identity,identity)),
    inference(symmetry,[status(thm)],[c350]) ).

cnf(c352,plain,
    inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))) = multiply(inverse(double_divide(double_divide(identity,identity),X)),double_divide(identity,identity)),
    inference(substitution,[status(thm)],[c193]) ).

cnf(c353,plain,
    multiply(inverse(double_divide(double_divide(identity,identity),X)),double_divide(identity,identity)) = inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))),
    inference(symmetry,[status(thm)],[c352]) ).

cnf(c354,plain,
    multiply(inverse(double_divide(double_divide(identity,identity),X)),double_divide(identity,identity)) = X,
    inference(transitivity,[status(thm)],[c353,c113]) ).

cnf(c355,plain,
    inverse(inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X)))))) = X,
    inference(transitivity,[status(thm)],[c351,c354]) ).

cnf(c356,plain,
    inverse(inverse(inverse(inverse(multiply(X,double_divide(identity,identity)))))) = X,
    inference(transitivity,[status(thm)],[c349,c355]) ).

cnf(c357,plain,
    inverse(inverse(inverse(multiply(inverse(X),double_divide(identity,identity))))) = X,
    inference(transitivity,[status(thm)],[c343,c356]) ).

cnf(c358,plain,
    inverse(inverse(multiply(inverse(inverse(X)),double_divide(identity,identity)))) = X,
    inference(transitivity,[status(thm)],[c340,c357]) ).

cnf(c359,plain,
    inverse(multiply(inverse(inverse(inverse(X))),double_divide(identity,identity))) = X,
    inference(transitivity,[status(thm)],[c337,c358]) ).

cnf(c360,plain,
    multiply(inverse(inverse(inverse(inverse(X)))),double_divide(identity,identity)) = X,
    inference(transitivity,[status(thm)],[c335,c359]) ).

cnf(c361,plain,
    inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(X)))))))) = X,
    inference(transitivity,[status(thm)],[c333,c360]) ).

cnf(c362,plain,
    inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X))))))))) = double_divide(double_divide(identity,identity),X),
    inference(substitution,[status(thm)],[c361]) ).

cnf(c363,plain,
    multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X))))))))),X) = multiply(double_divide(double_divide(identity,identity),X),X),
    inference(congruence,[status(thm)],[c362]) ).

cnf(c364,plain,
    multiply(double_divide(double_divide(identity,identity),X),X) = multiply(inverse(inverse(inverse(X))),X),
    inference(congruence,[status(thm)],[c150]) ).

cnf(c365,plain,
    multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X))))))))),X) = multiply(inverse(inverse(inverse(X))),X),
    inference(transitivity,[status(thm)],[c363,c364]) ).

cnf(c366,plain,
    multiply(multiply(inverse(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X))))),double_divide(identity,identity)),X) = multiply(inverse(inverse(inverse(X))),X),
    inference(transitivity,[status(thm)],[c331,c365]) ).

cnf(c367,plain,
    multiply(inverse(multiply(inverse(inverse(inverse(double_divide(double_divide(identity,identity),X)))),double_divide(identity,identity))),X) = multiply(inverse(inverse(inverse(X))),X),
    inference(transitivity,[status(thm)],[c329,c366]) ).

cnf(c368,plain,
    multiply(inverse(inverse(multiply(inverse(inverse(double_divide(double_divide(identity,identity),X))),double_divide(identity,identity)))),X) = multiply(inverse(inverse(inverse(X))),X),
    inference(transitivity,[status(thm)],[c327,c367]) ).

cnf(c369,plain,
    multiply(inverse(inverse(inverse(multiply(inverse(double_divide(double_divide(identity,identity),X)),double_divide(identity,identity))))),X) = multiply(inverse(inverse(inverse(X))),X),
    inference(transitivity,[status(thm)],[c325,c368]) ).

cnf(c370,plain,
    multiply(inverse(inverse(inverse(inverse(multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity)))))),X) = multiply(inverse(inverse(inverse(X))),X),
    inference(transitivity,[status(thm)],[c322,c369]) ).

cnf(c371,plain,
    inverse(inverse(inverse(inverse(inverse(inverse(multiply(X,multiply(double_divide(double_divide(identity,identity),X),double_divide(identity,identity))))))))) = multiply(inverse(inverse(inverse(X))),X),
    inference(transitivity,[status(thm)],[c318,c370]) ).

cnf(c372,plain,
    inverse(inverse(inverse(inverse(inverse(inverse(double_divide(identity,identity))))))) = multiply(inverse(inverse(inverse(X))),X),
    inference(transitivity,[status(thm)],[c317,c371]) ).

cnf(c373,plain,
    inverse(inverse(inverse(inverse(inverse(double_divide(identity,identity)))))) = multiply(inverse(inverse(inverse(X))),X),
    inference(transitivity,[status(thm)],[c298,c372]) ).

cnf(c374,plain,
    inverse(inverse(inverse(inverse(double_divide(identity,identity))))) = multiply(inverse(inverse(inverse(X))),X),
    inference(transitivity,[status(thm)],[c292,c373]) ).

cnf(c375,plain,
    inverse(inverse(inverse(double_divide(identity,identity)))) = multiply(inverse(inverse(inverse(X))),X),
    inference(transitivity,[status(thm)],[c287,c374]) ).

cnf(c376,plain,
    inverse(inverse(double_divide(identity,identity))) = multiply(inverse(inverse(inverse(X))),X),
    inference(transitivity,[status(thm)],[c283,c375]) ).

cnf(c377,plain,
    inverse(double_divide(identity,identity)) = multiply(inverse(inverse(inverse(X))),X),
    inference(transitivity,[status(thm)],[c280,c376]) ).

cnf(c378,plain,
    double_divide(identity,identity) = multiply(inverse(inverse(inverse(X))),X),
    inference(transitivity,[status(thm)],[c278,c377]) ).

cnf(c379,plain,
    double_divide(double_divide(identity,X),double_divide(identity,identity)) = double_divide(double_divide(identity,X),multiply(inverse(inverse(inverse(X2))),X2)),
    inference(congruence,[status(thm)],[c378]) ).

cnf(c380,plain,
    double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),double_divide(identity,identity))) = double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),multiply(inverse(inverse(inverse(X2))),X2))),
    inference(congruence,[status(thm)],[c379]) ).

cnf(c381,plain,
    double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),multiply(inverse(inverse(inverse(X2))),X2))),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c380]) ).

cnf(c382,plain,
    inverse(double_divide(X,X2)) = multiply(X2,X),
    inference(substitution,[status(thm)],[c82]) ).

cnf(c383,plain,
    multiply(X2,X) = inverse(double_divide(X,X2)),
    inference(symmetry,[status(thm)],[c382]) ).

cnf(c384,plain,
    double_divide(double_divide(identity,X3),multiply(X2,X)) = double_divide(double_divide(identity,X3),inverse(double_divide(X,X2))),
    inference(congruence,[status(thm)],[c383]) ).

cnf(c385,plain,
    double_divide(double_divide(X3,identity),double_divide(double_divide(identity,X3),multiply(X2,X))) = double_divide(double_divide(X3,identity),double_divide(double_divide(identity,X3),inverse(double_divide(X,X2)))),
    inference(congruence,[status(thm)],[c384]) ).

cnf(c386,plain,
    double_divide(double_divide(double_divide(X3,identity),double_divide(double_divide(identity,X3),multiply(X2,X))),double_divide(identity,identity)) = double_divide(double_divide(double_divide(X3,identity),double_divide(double_divide(identity,X3),inverse(double_divide(X,X2)))),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c385]) ).

cnf(c387,plain,
    double_divide(double_divide(double_divide(X3,identity),double_divide(double_divide(identity,X3),inverse(double_divide(X,X2)))),double_divide(identity,identity)) = double_divide(X,X2),
    inference(substitution,[status(thm)],[c31]) ).

cnf(c388,plain,
    double_divide(double_divide(double_divide(X3,identity),double_divide(double_divide(identity,X3),multiply(X2,X))),double_divide(identity,identity)) = double_divide(X,X2),
    inference(transitivity,[status(thm)],[c386,c387]) ).

cnf(c389,plain,
    double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),multiply(inverse(inverse(inverse(X2))),X2))),double_divide(identity,identity)) = double_divide(X2,inverse(inverse(inverse(X2)))),
    inference(substitution,[status(thm)],[c388]) ).

cnf(c390,plain,
    double_divide(double_divide(double_divide(X,identity),double_divide(double_divide(identity,X),double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(X2,inverse(inverse(inverse(X2)))),
    inference(transitivity,[status(thm)],[c381,c389]) ).

cnf(c391,plain,
    identity = double_divide(X,inverse(inverse(inverse(X)))),
    inference(transitivity,[status(thm)],[c274,c390]) ).

cnf(c392,plain,
    double_divide(identity,identity) = double_divide(X,inverse(inverse(inverse(X)))),
    inference(transitivity,[status(thm)],[c70,c391]) ).

cnf(c393,plain,
    double_divide(identity,identity) = double_divide(inverse(inverse(inverse(multiply(identity,X)))),inverse(inverse(inverse(inverse(inverse(inverse(multiply(identity,X)))))))),
    inference(substitution,[status(thm)],[c392]) ).

cnf(c394,plain,
    double_divide(inverse(inverse(inverse(multiply(identity,X)))),inverse(inverse(inverse(inverse(inverse(inverse(multiply(identity,X)))))))) = double_divide(identity,identity),
    inference(symmetry,[status(thm)],[c393]) ).

cnf(c395,plain,
    double_divide(inverse(inverse(inverse(multiply(identity,X)))),X) = double_divide(identity,identity),
    inference(transitivity,[status(thm)],[c272,c394]) ).

cnf(c396,plain,
    double_divide(identity,identity) = double_divide(inverse(inverse(inverse(multiply(identity,X)))),X),
    inference(symmetry,[status(thm)],[c395]) ).

cnf(c397,plain,
    double_divide(X,double_divide(identity,identity)) = double_divide(X,double_divide(inverse(inverse(inverse(multiply(identity,X2)))),X2)),
    inference(congruence,[status(thm)],[c396]) ).

cnf(c398,plain,
    double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity))) = double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(inverse(inverse(inverse(multiply(identity,X2)))),X2))),
    inference(congruence,[status(thm)],[c397]) ).

cnf(c399,plain,
    double_divide(X2,double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity)))) = double_divide(X2,double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(inverse(inverse(inverse(multiply(identity,X2)))),X2)))),
    inference(congruence,[status(thm)],[c398]) ).

cnf(c400,plain,
    double_divide(double_divide(X2,double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity)))),double_divide(identity,identity)) = double_divide(double_divide(X2,double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(inverse(inverse(inverse(multiply(identity,X2)))),X2)))),double_divide(identity,identity)),
    inference(congruence,[status(thm)],[c399]) ).

cnf(c401,plain,
    double_divide(double_divide(X2,double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(inverse(inverse(inverse(multiply(identity,X2)))),X2)))),double_divide(identity,identity)) = X,
    inference(substitution,[status(thm)],[c5]) ).

cnf(c402,plain,
    double_divide(double_divide(X2,double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity)))),double_divide(identity,identity)) = X,
    inference(transitivity,[status(thm)],[c400,c401]) ).

cnf(c403,plain,
    inverse(double_divide(X2,double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity))))) = X,
    inference(transitivity,[status(thm)],[c270,c402]) ).

cnf(c404,plain,
    multiply(double_divide(double_divide(identity,inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity))),X2) = X,
    inference(transitivity,[status(thm)],[c268,c403]) ).

cnf(c405,plain,
    multiply(double_divide(double_divide(double_divide(identity,identity),inverse(inverse(inverse(multiply(identity,X2))))),double_divide(X,double_divide(identity,identity))),X2) = X,
    inference(transitivity,[status(thm)],[c266,c404]) ).

cnf(c406,plain,
    multiply(double_divide(inverse(inverse(inverse(inverse(inverse(inverse(multiply(identity,X2))))))),double_divide(X,double_divide(identity,identity))),X2) = X,
    inference(transitivity,[status(thm)],[c263,c405]) ).

cnf(c407,plain,
    multiply(double_divide(X2,double_divide(X,double_divide(identity,identity))),X2) = X,
    inference(transitivity,[status(thm)],[c259,c406]) ).

cnf(c408,plain,
    multiply(double_divide(X2,inverse(X)),X2) = X,
    inference(transitivity,[status(thm)],[c77,c407]) ).

cnf(c409,plain,
    multiply(double_divide(X,inverse(X)),X) = X,
    inference(substitution,[status(thm)],[c408]) ).

cnf(c410,plain,
    multiply(identity,X) = X,
    inference(transitivity,[status(thm)],[c4,c409]) ).

cnf(c411,plain,
    multiply(identity,a2) = a2,
    inference(substitution,[status(thm)],[c410]) ).

cnf(c412,plain,
    $false,
    inference(resolution,[status(thm)],[c1,c411]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : GRP582-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35  % Computer : n018.cluster.edu
% 0.10/0.35  % Model    : x86_64 x86_64
% 0.10/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35  % Memory   : 8046.5625MB
% 0.10/0.35  % OS       : Linux 6.8.0-71-generic
% 0.10/0.35  % CPULimit : 300
% 0.10/0.35  % WCLimit  : 300
% 0.10/0.35  % DateTime : Sun Sep 27 10:09:52 UTC 2026
% 0.10/0.35  % CPUTime  : 
% 0.10/0.35  Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.46  Command-line arguments: --flatten --complete-subsets
% 0.13/0.46  
% 0.13/0.46  % SZS status Unsatisfiable
% 0.13/0.46  
% 0.57/0.50  % SZS output start CNFRefutation
% See solution above
% 1.25/0.69  
% 1.25/0.69  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------