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Twee---2.7.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : GRP122-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n013.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 10:09:18 AM UTC 2026

% Result   : Unsatisfiable 0.78s 0.61s
% Output   : CNFRefutation 3.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :  108
%            Number of leaves      :    3
% Syntax   : Number of clauses     :  471 ( 471 unt;   0 nHn;  34 RR)
%            Number of literals    :  471 ( 470 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :  650 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
    multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_order3) ).

cnf(c2,axiom,
    multiply(identity,identity) = identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).

cnf(c3,plain,
    identity = multiply(identity,identity),
    inference(symmetry,[status(thm)],[c2]) ).

cnf(c4,plain,
    multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),identity) = multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,identity)),
    inference(congruence,[status(thm)],[c3]) ).

cnf(c5,plain,
    multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),identity)) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,identity))),
    inference(congruence,[status(thm)],[c4]) ).

cnf(c6,plain,
    identity = multiply(identity,identity),
    inference(symmetry,[status(thm)],[c2]) ).

cnf(c7,plain,
    multiply(identity,identity) = multiply(identity,multiply(identity,identity)),
    inference(congruence,[status(thm)],[c6]) ).

cnf(c8,plain,
    multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,identity)) = multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,multiply(identity,identity))),
    inference(congruence,[status(thm)],[c7]) ).

cnf(c9,plain,
    multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,identity))) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,multiply(identity,identity)))),
    inference(congruence,[status(thm)],[c8]) ).

cnf(c10,axiom,
    multiply(Y,multiply(multiply(Y,multiply(multiply(Y,Y),multiply(X,Z))),multiply(Z,multiply(Z,Z)))) = X,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).

cnf(c11,plain,
    multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,multiply(identity,identity)))) = X2,
    inference(substitution,[status(thm)],[c10]) ).

cnf(c12,plain,
    multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),multiply(identity,identity))) = X2,
    inference(transitivity,[status(thm)],[c9,c11]) ).

cnf(c13,plain,
    multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),identity)) = X2,
    inference(transitivity,[status(thm)],[c5,c12]) ).

cnf(c14,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X2,identity))),identity)) = X2,
    inference(substitution,[status(thm)],[c13]) ).

cnf(c15,plain,
    X2 = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X2,identity))),identity)),
    inference(symmetry,[status(thm)],[c14]) ).

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

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

cnf(c18,plain,
    multiply(identity,multiply(multiply(identity,X2),identity)) = multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X2,identity))),identity))),identity)),
    inference(congruence,[status(thm)],[c17]) ).

cnf(c19,plain,
    identity = multiply(identity,identity),
    inference(symmetry,[status(thm)],[c2]) ).

cnf(c20,plain,
    multiply(identity,multiply(X2,identity)) = multiply(multiply(identity,identity),multiply(X2,identity)),
    inference(congruence,[status(thm)],[c19]) ).

cnf(c21,plain,
    multiply(identity,multiply(identity,multiply(X2,identity))) = multiply(identity,multiply(multiply(identity,identity),multiply(X2,identity))),
    inference(congruence,[status(thm)],[c20]) ).

cnf(c22,plain,
    multiply(multiply(identity,multiply(identity,multiply(X2,identity))),identity) = multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X2,identity))),identity),
    inference(congruence,[status(thm)],[c21]) ).

cnf(c23,plain,
    multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X2,identity))),identity)) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X2,identity))),identity)),
    inference(congruence,[status(thm)],[c22]) ).

cnf(c24,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X2,identity))),identity)) = X2,
    inference(substitution,[status(thm)],[c13]) ).

cnf(c25,plain,
    multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X2,identity))),identity)) = X2,
    inference(transitivity,[status(thm)],[c23,c24]) ).

cnf(c26,plain,
    multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X2,identity))),identity))),identity)) = multiply(identity,multiply(multiply(identity,identity),multiply(X2,identity))),
    inference(substitution,[status(thm)],[c25]) ).

cnf(c27,plain,
    multiply(multiply(identity,identity),multiply(X2,identity)) = multiply(identity,multiply(X2,identity)),
    inference(congruence,[status(thm)],[c2]) ).

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

cnf(c29,plain,
    multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X2,identity))),identity))),identity)) = multiply(identity,multiply(identity,multiply(X2,identity))),
    inference(transitivity,[status(thm)],[c26,c28]) ).

cnf(c30,plain,
    multiply(identity,multiply(multiply(identity,X2),identity)) = multiply(identity,multiply(identity,multiply(X2,identity))),
    inference(transitivity,[status(thm)],[c18,c29]) ).

cnf(c31,plain,
    multiply(identity,multiply(multiply(identity,multiply(X2,identity)),identity)) = multiply(identity,multiply(identity,multiply(multiply(X2,identity),identity))),
    inference(substitution,[status(thm)],[c30]) ).

cnf(c32,plain,
    multiply(identity,multiply(identity,multiply(multiply(X2,identity),identity))) = multiply(identity,multiply(multiply(identity,multiply(X2,identity)),identity)),
    inference(symmetry,[status(thm)],[c31]) ).

cnf(c33,plain,
    multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X2,identity),identity)))) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,identity)),identity))),
    inference(congruence,[status(thm)],[c32]) ).

cnf(c34,plain,
    identity = multiply(identity,identity),
    inference(symmetry,[status(thm)],[c2]) ).

cnf(c35,plain,
    multiply(identity,multiply(X2,identity)) = multiply(multiply(identity,identity),multiply(X2,identity)),
    inference(congruence,[status(thm)],[c34]) ).

cnf(c36,plain,
    multiply(multiply(identity,multiply(X2,identity)),identity) = multiply(multiply(multiply(identity,identity),multiply(X2,identity)),identity),
    inference(congruence,[status(thm)],[c35]) ).

cnf(c37,plain,
    multiply(identity,multiply(multiply(identity,multiply(X2,identity)),identity)) = multiply(identity,multiply(multiply(multiply(identity,identity),multiply(X2,identity)),identity)),
    inference(congruence,[status(thm)],[c36]) ).

cnf(c38,plain,
    multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,identity)),identity))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,identity),multiply(X2,identity)),identity))),
    inference(congruence,[status(thm)],[c37]) ).

cnf(c39,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X2,identity))),identity)) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,identity),multiply(X2,identity)),identity))),
    inference(substitution,[status(thm)],[c30]) ).

cnf(c40,plain,
    multiply(identity,multiply(identity,multiply(multiply(multiply(identity,identity),multiply(X2,identity)),identity))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X2,identity))),identity)),
    inference(symmetry,[status(thm)],[c39]) ).

cnf(c41,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X2,identity))),identity)) = X2,
    inference(substitution,[status(thm)],[c13]) ).

cnf(c42,plain,
    multiply(identity,multiply(identity,multiply(multiply(multiply(identity,identity),multiply(X2,identity)),identity))) = X2,
    inference(transitivity,[status(thm)],[c40,c41]) ).

cnf(c43,plain,
    multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,identity)),identity))) = X2,
    inference(transitivity,[status(thm)],[c38,c42]) ).

cnf(c44,plain,
    multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X2,identity),identity)))) = X2,
    inference(transitivity,[status(thm)],[c33,c43]) ).

cnf(c45,plain,
    multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(X2,X2),identity),identity),identity)))) = multiply(multiply(X2,X2),identity),
    inference(substitution,[status(thm)],[c44]) ).

cnf(c46,plain,
    multiply(multiply(X2,X2),identity) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(X2,X2),identity),identity),identity)))),
    inference(symmetry,[status(thm)],[c45]) ).

cnf(c47,plain,
    identity = multiply(identity,identity),
    inference(symmetry,[status(thm)],[c2]) ).

cnf(c48,plain,
    multiply(multiply(X3,multiply(multiply(X3,X2),identity)),identity) = multiply(multiply(X3,multiply(multiply(X3,X2),identity)),multiply(identity,identity)),
    inference(congruence,[status(thm)],[c47]) ).

cnf(c49,plain,
    multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,X2),identity)),identity)) = multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,X2),identity)),multiply(identity,identity))),
    inference(congruence,[status(thm)],[c48]) ).

cnf(c50,plain,
    identity = multiply(identity,identity),
    inference(symmetry,[status(thm)],[c2]) ).

cnf(c51,plain,
    multiply(identity,identity) = multiply(identity,multiply(identity,identity)),
    inference(congruence,[status(thm)],[c50]) ).

cnf(c52,plain,
    multiply(multiply(X3,multiply(multiply(X3,X2),identity)),multiply(identity,identity)) = multiply(multiply(X3,multiply(multiply(X3,X2),identity)),multiply(identity,multiply(identity,identity))),
    inference(congruence,[status(thm)],[c51]) ).

cnf(c53,plain,
    multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,X2),identity)),multiply(identity,identity))) = multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,X2),identity)),multiply(identity,multiply(identity,identity)))),
    inference(congruence,[status(thm)],[c52]) ).

cnf(c54,plain,
    multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,identity))),identity))),multiply(identity,multiply(identity,identity)))) = multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,identity))),
    inference(substitution,[status(thm)],[c10]) ).

cnf(c55,plain,
    multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,identity))) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,identity))),identity))),multiply(identity,multiply(identity,identity)))),
    inference(symmetry,[status(thm)],[c54]) ).

cnf(c56,plain,
    multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,identity))),identity)) = X2,
    inference(substitution,[status(thm)],[c13]) ).

cnf(c57,plain,
    multiply(X3,multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,identity))),identity))) = multiply(X3,X2),
    inference(congruence,[status(thm)],[c56]) ).

cnf(c58,plain,
    multiply(multiply(X3,multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,identity))),identity))),multiply(identity,multiply(identity,identity))) = multiply(multiply(X3,X2),multiply(identity,multiply(identity,identity))),
    inference(congruence,[status(thm)],[c57]) ).

cnf(c59,plain,
    multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,identity))),identity))),multiply(identity,multiply(identity,identity)))) = multiply(X3,multiply(multiply(X3,X2),multiply(identity,multiply(identity,identity)))),
    inference(congruence,[status(thm)],[c58]) ).

cnf(c60,plain,
    multiply(identity,multiply(identity,identity)) = multiply(identity,identity),
    inference(congruence,[status(thm)],[c2]) ).

cnf(c61,plain,
    multiply(multiply(X3,X2),multiply(identity,multiply(identity,identity))) = multiply(multiply(X3,X2),multiply(identity,identity)),
    inference(congruence,[status(thm)],[c60]) ).

cnf(c62,plain,
    multiply(X3,multiply(multiply(X3,X2),multiply(identity,multiply(identity,identity)))) = multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),
    inference(congruence,[status(thm)],[c61]) ).

cnf(c63,plain,
    multiply(multiply(X3,X2),multiply(identity,identity)) = multiply(multiply(X3,X2),identity),
    inference(congruence,[status(thm)],[c2]) ).

cnf(c64,plain,
    multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))) = multiply(X3,multiply(multiply(X3,X2),identity)),
    inference(congruence,[status(thm)],[c63]) ).

cnf(c65,plain,
    multiply(X3,multiply(multiply(X3,X2),multiply(identity,multiply(identity,identity)))) = multiply(X3,multiply(multiply(X3,X2),identity)),
    inference(transitivity,[status(thm)],[c62,c64]) ).

cnf(c66,plain,
    multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,identity))),identity))),multiply(identity,multiply(identity,identity)))) = multiply(X3,multiply(multiply(X3,X2),identity)),
    inference(transitivity,[status(thm)],[c59,c65]) ).

cnf(c67,plain,
    multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,identity))) = multiply(X3,multiply(multiply(X3,X2),identity)),
    inference(transitivity,[status(thm)],[c55,c66]) ).

cnf(c68,plain,
    multiply(X3,multiply(multiply(X3,X2),identity)) = multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,identity))),
    inference(symmetry,[status(thm)],[c67]) ).

cnf(c69,plain,
    multiply(multiply(X3,multiply(multiply(X3,X2),identity)),multiply(identity,multiply(identity,identity))) = multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,identity))),multiply(identity,multiply(identity,identity))),
    inference(congruence,[status(thm)],[c68]) ).

cnf(c70,plain,
    multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,X2),identity)),multiply(identity,multiply(identity,identity)))) = multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,identity))),multiply(identity,multiply(identity,identity)))),
    inference(congruence,[status(thm)],[c69]) ).

cnf(c71,plain,
    multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,identity))),multiply(identity,multiply(identity,identity)))) = X2,
    inference(substitution,[status(thm)],[c10]) ).

cnf(c72,plain,
    multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,X2),identity)),multiply(identity,multiply(identity,identity)))) = X2,
    inference(transitivity,[status(thm)],[c70,c71]) ).

cnf(c73,plain,
    multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,X2),identity)),multiply(identity,identity))) = X2,
    inference(transitivity,[status(thm)],[c53,c72]) ).

cnf(c74,plain,
    multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,X2),identity)),identity)) = X2,
    inference(transitivity,[status(thm)],[c49,c73]) ).

cnf(c75,plain,
    multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,identity),multiply(X2,X4))),identity)),identity)) = multiply(multiply(X3,identity),multiply(X2,X4)),
    inference(substitution,[status(thm)],[c74]) ).

cnf(c76,plain,
    multiply(multiply(X4,identity),multiply(X3,X2)) = multiply(multiply(X4,X4),multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,identity),multiply(X3,X2))),identity)),identity)),
    inference(symmetry,[status(thm)],[c75]) ).

cnf(c77,plain,
    identity = multiply(identity,identity),
    inference(symmetry,[status(thm)],[c2]) ).

cnf(c78,plain,
    multiply(identity,multiply(X3,X2)) = multiply(multiply(identity,identity),multiply(X3,X2)),
    inference(congruence,[status(thm)],[c77]) ).

cnf(c79,plain,
    multiply(identity,multiply(identity,multiply(X3,X2))) = multiply(identity,multiply(multiply(identity,identity),multiply(X3,X2))),
    inference(congruence,[status(thm)],[c78]) ).

cnf(c80,plain,
    multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2))) = multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2))),
    inference(congruence,[status(thm)],[c79]) ).

cnf(c81,plain,
    multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2)))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),
    inference(congruence,[status(thm)],[c80]) ).

cnf(c82,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))) = X3,
    inference(substitution,[status(thm)],[c10]) ).

cnf(c83,plain,
    multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2)))) = X3,
    inference(transitivity,[status(thm)],[c81,c82]) ).

cnf(c84,plain,
    X3 = multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),
    inference(symmetry,[status(thm)],[c83]) ).

cnf(c85,plain,
    multiply(multiply(multiply(X4,X4),multiply(X4,X4)),X3) = multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),
    inference(congruence,[status(thm)],[c84]) ).

cnf(c86,plain,
    multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),X3)) = multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2)))))),
    inference(congruence,[status(thm)],[c85]) ).

cnf(c87,plain,
    multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))) = multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))),
    inference(substitution,[status(thm)],[c10]) ).

cnf(c88,plain,
    multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))) = multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))),
    inference(symmetry,[status(thm)],[c87]) ).

cnf(c89,plain,
    multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))) = X3,
    inference(substitution,[status(thm)],[c10]) ).

cnf(c90,plain,
    multiply(X4,multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))) = multiply(X4,X3),
    inference(congruence,[status(thm)],[c89]) ).

cnf(c91,plain,
    multiply(multiply(X4,multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(multiply(X4,X3),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),
    inference(congruence,[status(thm)],[c90]) ).

cnf(c92,plain,
    multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))) = multiply(X4,multiply(multiply(X4,X3),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))),
    inference(congruence,[status(thm)],[c91]) ).

cnf(c93,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X2),identity)),identity)) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X2),identity),identity))),
    inference(substitution,[status(thm)],[c30]) ).

cnf(c94,plain,
    multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X2),identity),identity))) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X2),identity)),identity)),
    inference(symmetry,[status(thm)],[c93]) ).

cnf(c95,plain,
    multiply(multiply(identity,multiply(multiply(identity,X2),identity)),identity) = multiply(multiply(identity,multiply(identity,multiply(X2,identity))),identity),
    inference(congruence,[status(thm)],[c30]) ).

cnf(c96,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X2),identity)),identity)) = multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X2,identity))),identity)),
    inference(congruence,[status(thm)],[c95]) ).

cnf(c97,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X2),identity)),identity)) = X2,
    inference(transitivity,[status(thm)],[c96,c25]) ).

cnf(c98,plain,
    multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X2),identity),identity))) = X2,
    inference(transitivity,[status(thm)],[c94,c97]) ).

cnf(c99,plain,
    multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),identity),identity))) = multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))),
    inference(substitution,[status(thm)],[c98]) ).

cnf(c100,plain,
    multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),identity),identity))),
    inference(symmetry,[status(thm)],[c99]) ).

cnf(c101,plain,
    identity = multiply(identity,identity),
    inference(symmetry,[status(thm)],[c2]) ).

cnf(c102,plain,
    multiply(identity,multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(multiply(identity,identity),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),
    inference(congruence,[status(thm)],[c101]) ).

cnf(c103,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))) = X3,
    inference(substitution,[status(thm)],[c10]) ).

cnf(c104,plain,
    X3 = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),
    inference(symmetry,[status(thm)],[c103]) ).

cnf(c105,plain,
    multiply(identity,X3) = multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),
    inference(congruence,[status(thm)],[c104]) ).

cnf(c106,plain,
    multiply(multiply(identity,X3),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),
    inference(congruence,[status(thm)],[c105]) ).

cnf(c107,plain,
    multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),identity)),identity)) = multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2))),
    inference(substitution,[status(thm)],[c74]) ).

cnf(c108,plain,
    multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2))) = multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),identity)),identity)),
    inference(symmetry,[status(thm)],[c107]) ).

cnf(c109,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),identity) = multiply(X3,identity),
    inference(congruence,[status(thm)],[c83]) ).

cnf(c110,plain,
    multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),identity)) = multiply(identity,multiply(X3,identity)),
    inference(congruence,[status(thm)],[c109]) ).

cnf(c111,plain,
    multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),identity)),identity) = multiply(multiply(identity,multiply(X3,identity)),identity),
    inference(congruence,[status(thm)],[c110]) ).

cnf(c112,plain,
    multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),identity)),identity)) = multiply(multiply(identity,identity),multiply(multiply(identity,multiply(X3,identity)),identity)),
    inference(congruence,[status(thm)],[c111]) ).

cnf(c113,plain,
    multiply(multiply(identity,identity),multiply(multiply(identity,multiply(X2,identity)),identity)) = multiply(identity,multiply(multiply(identity,multiply(X2,identity)),identity)),
    inference(congruence,[status(thm)],[c2]) ).

cnf(c114,plain,
    multiply(identity,multiply(multiply(identity,multiply(X2,identity)),identity)) = multiply(identity,multiply(identity,multiply(multiply(X2,identity),identity))),
    inference(substitution,[status(thm)],[c30]) ).

cnf(c115,plain,
    multiply(multiply(identity,identity),multiply(multiply(identity,multiply(X2,identity)),identity)) = multiply(identity,multiply(identity,multiply(multiply(X2,identity),identity))),
    inference(transitivity,[status(thm)],[c113,c114]) ).

cnf(c116,plain,
    multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2)))),identity)),identity)) = multiply(identity,multiply(identity,multiply(multiply(X3,identity),identity))),
    inference(transitivity,[status(thm)],[c112,c115]) ).

cnf(c117,plain,
    multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2))) = multiply(identity,multiply(identity,multiply(multiply(X3,identity),identity))),
    inference(transitivity,[status(thm)],[c108,c116]) ).

cnf(c118,plain,
    multiply(multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X3,X2))),identity),identity))),
    inference(substitution,[status(thm)],[c117]) ).

cnf(c119,plain,
    multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X3,X2))),identity),identity))) = multiply(multiply(identity,identity),multiply(X3,X2)),
    inference(substitution,[status(thm)],[c98]) ).

cnf(c120,plain,
    multiply(multiply(identity,identity),multiply(X3,X2)) = multiply(identity,multiply(X3,X2)),
    inference(congruence,[status(thm)],[c2]) ).

cnf(c121,plain,
    multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X3,X2))),identity),identity))) = multiply(identity,multiply(X3,X2)),
    inference(transitivity,[status(thm)],[c119,c120]) ).

cnf(c122,plain,
    multiply(multiply(identity,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,identity),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(identity,multiply(X3,X2)),
    inference(transitivity,[status(thm)],[c118,c121]) ).

cnf(c123,plain,
    multiply(multiply(identity,X3),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(identity,multiply(X3,X2)),
    inference(transitivity,[status(thm)],[c106,c122]) ).

cnf(c124,plain,
    multiply(multiply(identity,identity),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(identity,multiply(identity,X2)),
    inference(substitution,[status(thm)],[c123]) ).

cnf(c125,plain,
    multiply(identity,multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(identity,multiply(identity,X2)),
    inference(transitivity,[status(thm)],[c102,c124]) ).

cnf(c126,plain,
    multiply(multiply(identity,multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),identity) = multiply(multiply(identity,multiply(identity,X2)),identity),
    inference(congruence,[status(thm)],[c125]) ).

cnf(c127,plain,
    multiply(multiply(multiply(identity,multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),identity),identity) = multiply(multiply(multiply(identity,multiply(identity,X2)),identity),identity),
    inference(congruence,[status(thm)],[c126]) ).

cnf(c128,plain,
    multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),identity),identity)) = multiply(identity,multiply(multiply(multiply(identity,multiply(identity,X2)),identity),identity)),
    inference(congruence,[status(thm)],[c127]) ).

cnf(c129,plain,
    multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),identity),identity))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(identity,X2)),identity),identity))),
    inference(congruence,[status(thm)],[c128]) ).

cnf(c130,plain,
    multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(identity,X2)),identity),identity))) = multiply(identity,X2),
    inference(substitution,[status(thm)],[c98]) ).

cnf(c131,plain,
    multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))),identity),identity))) = multiply(identity,X2),
    inference(transitivity,[status(thm)],[c129,c130]) ).

cnf(c132,plain,
    multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))) = multiply(identity,X2),
    inference(transitivity,[status(thm)],[c100,c131]) ).

cnf(c133,plain,
    multiply(multiply(X4,X3),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))))) = multiply(multiply(X4,X3),multiply(identity,X2)),
    inference(congruence,[status(thm)],[c132]) ).

cnf(c134,plain,
    multiply(X4,multiply(multiply(X4,X3),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))) = multiply(X4,multiply(multiply(X4,X3),multiply(identity,X2))),
    inference(congruence,[status(thm)],[c133]) ).

cnf(c135,plain,
    multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))),multiply(X2,multiply(X2,X2))))),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))) = multiply(X4,multiply(multiply(X4,X3),multiply(identity,X2))),
    inference(transitivity,[status(thm)],[c92,c134]) ).

cnf(c136,plain,
    multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))) = multiply(X4,multiply(multiply(X4,X3),multiply(identity,X2))),
    inference(transitivity,[status(thm)],[c88,c135]) ).

cnf(c137,plain,
    multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2)))))) = multiply(X4,multiply(multiply(X4,identity),multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2)))))),
    inference(substitution,[status(thm)],[c136]) ).

cnf(c138,plain,
    multiply(multiply(X4,identity),multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2))))) = multiply(multiply(X4,identity),X3),
    inference(congruence,[status(thm)],[c83]) ).

cnf(c139,plain,
    multiply(X4,multiply(multiply(X4,identity),multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2)))))) = multiply(X4,multiply(multiply(X4,identity),X3)),
    inference(congruence,[status(thm)],[c138]) ).

cnf(c140,plain,
    multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X3,X2))),multiply(X2,multiply(X2,X2)))))) = multiply(X4,multiply(multiply(X4,identity),X3)),
    inference(transitivity,[status(thm)],[c137,c139]) ).

cnf(c141,plain,
    multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),X2)) = multiply(X3,multiply(multiply(X3,identity),X2)),
    inference(transitivity,[status(thm)],[c86,c140]) ).

cnf(c142,plain,
    multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))) = multiply(X4,multiply(multiply(X4,identity),multiply(X3,X2))),
    inference(substitution,[status(thm)],[c141]) ).

cnf(c143,plain,
    multiply(X4,multiply(multiply(X4,identity),multiply(X3,X2))) = multiply(multiply(X4,X4),multiply(multiply(multiply(X4,X4),multiply(X4,X4)),multiply(X3,X2))),
    inference(symmetry,[status(thm)],[c142]) ).

cnf(c144,plain,
    multiply(X4,multiply(multiply(X4,identity),multiply(X3,X2))) = multiply(X4,multiply(multiply(X4,X3),multiply(identity,X2))),
    inference(transitivity,[status(thm)],[c143,c136]) ).

cnf(c145,plain,
    multiply(multiply(X4,multiply(multiply(X4,identity),multiply(X3,X2))),identity) = multiply(multiply(X4,multiply(multiply(X4,X3),multiply(identity,X2))),identity),
    inference(congruence,[status(thm)],[c144]) ).

cnf(c146,plain,
    multiply(X4,multiply(multiply(X4,multiply(multiply(X4,identity),multiply(X3,X2))),identity)) = multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X3),multiply(identity,X2))),identity)),
    inference(congruence,[status(thm)],[c145]) ).

cnf(c147,plain,
    multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,identity),multiply(X3,X2))),identity)),identity) = multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X3),multiply(identity,X2))),identity)),identity),
    inference(congruence,[status(thm)],[c146]) ).

cnf(c148,plain,
    multiply(multiply(X4,X4),multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,identity),multiply(X3,X2))),identity)),identity)) = multiply(multiply(X4,X4),multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X3),multiply(identity,X2))),identity)),identity)),
    inference(congruence,[status(thm)],[c147]) ).

cnf(c149,plain,
    multiply(multiply(X4,X4),multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X3),multiply(identity,X2))),identity)),identity)) = multiply(multiply(X4,X3),multiply(identity,X2)),
    inference(substitution,[status(thm)],[c74]) ).

cnf(c150,plain,
    multiply(multiply(X4,X4),multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,identity),multiply(X3,X2))),identity)),identity)) = multiply(multiply(X4,X3),multiply(identity,X2)),
    inference(transitivity,[status(thm)],[c148,c149]) ).

cnf(c151,plain,
    multiply(multiply(X4,identity),multiply(X3,X2)) = multiply(multiply(X4,X3),multiply(identity,X2)),
    inference(transitivity,[status(thm)],[c76,c150]) ).

cnf(c152,plain,
    multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity))) = multiply(multiply(X2,multiply(X2,X2)),multiply(identity,multiply(multiply(X2,identity),identity))),
    inference(substitution,[status(thm)],[c151]) ).

cnf(c153,plain,
    multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X2),identity),identity))),identity)) = multiply(multiply(identity,X2),identity),
    inference(substitution,[status(thm)],[c25]) ).

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

cnf(c155,plain,
    multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X2),identity),identity))),identity) = multiply(X2,identity),
    inference(congruence,[status(thm)],[c98]) ).

cnf(c156,plain,
    multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X2),identity),identity))),identity)) = multiply(identity,multiply(X2,identity)),
    inference(congruence,[status(thm)],[c155]) ).

cnf(c157,plain,
    multiply(multiply(identity,X2),identity) = multiply(identity,multiply(X2,identity)),
    inference(transitivity,[status(thm)],[c154,c156]) ).

cnf(c158,plain,
    multiply(multiply(identity,multiply(X2,identity)),identity) = multiply(identity,multiply(multiply(X2,identity),identity)),
    inference(substitution,[status(thm)],[c157]) ).

cnf(c159,plain,
    multiply(identity,multiply(multiply(X2,identity),identity)) = multiply(multiply(identity,multiply(X2,identity)),identity),
    inference(symmetry,[status(thm)],[c158]) ).

cnf(c160,plain,
    multiply(multiply(X2,multiply(X2,X2)),multiply(identity,multiply(multiply(X2,identity),identity))) = multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(identity,multiply(X2,identity)),identity)),
    inference(congruence,[status(thm)],[c159]) ).

cnf(c161,plain,
    multiply(identity,multiply(X2,identity)) = multiply(multiply(identity,X2),identity),
    inference(symmetry,[status(thm)],[c157]) ).

cnf(c162,plain,
    multiply(multiply(identity,multiply(X2,identity)),identity) = multiply(multiply(multiply(identity,X2),identity),identity),
    inference(congruence,[status(thm)],[c161]) ).

cnf(c163,plain,
    multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(identity,multiply(X2,identity)),identity)) = multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(multiply(identity,X2),identity),identity)),
    inference(congruence,[status(thm)],[c162]) ).

cnf(c164,plain,
    multiply(identity,X2) = multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))),
    inference(symmetry,[status(thm)],[c132]) ).

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

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

cnf(c167,plain,
    multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(multiply(identity,X2),identity),identity)) = multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))),identity),identity)),
    inference(congruence,[status(thm)],[c166]) ).

cnf(c168,plain,
    multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,identity),multiply(X2,identity))),identity)),identity)) = multiply(multiply(X3,identity),multiply(X2,identity)),
    inference(substitution,[status(thm)],[c74]) ).

cnf(c169,plain,
    multiply(multiply(X3,identity),multiply(X2,identity)) = multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,identity),multiply(X2,identity))),identity)),identity)),
    inference(symmetry,[status(thm)],[c168]) ).

cnf(c170,plain,
    multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,identity))) = multiply(X3,multiply(multiply(X3,identity),multiply(X2,identity))),
    inference(substitution,[status(thm)],[c141]) ).

cnf(c171,plain,
    multiply(X3,multiply(multiply(X3,identity),multiply(X2,identity))) = multiply(multiply(X3,X3),multiply(multiply(multiply(X3,X3),multiply(X3,X3)),multiply(X2,identity))),
    inference(symmetry,[status(thm)],[c170]) ).

cnf(c172,plain,
    multiply(X3,multiply(multiply(X3,identity),multiply(X2,identity))) = multiply(X3,multiply(multiply(X3,X2),identity)),
    inference(transitivity,[status(thm)],[c171,c67]) ).

cnf(c173,plain,
    multiply(multiply(X3,multiply(multiply(X3,identity),multiply(X2,identity))),identity) = multiply(multiply(X3,multiply(multiply(X3,X2),identity)),identity),
    inference(congruence,[status(thm)],[c172]) ).

cnf(c174,plain,
    multiply(X3,multiply(multiply(X3,multiply(multiply(X3,identity),multiply(X2,identity))),identity)) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X2),identity)),identity)),
    inference(congruence,[status(thm)],[c173]) ).

cnf(c175,plain,
    multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,identity),multiply(X2,identity))),identity)),identity) = multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X2),identity)),identity)),identity),
    inference(congruence,[status(thm)],[c174]) ).

cnf(c176,plain,
    multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,identity),multiply(X2,identity))),identity)),identity)) = multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X2),identity)),identity)),identity)),
    inference(congruence,[status(thm)],[c175]) ).

cnf(c177,plain,
    multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X2),identity)),identity)),identity)) = multiply(multiply(X3,X2),identity),
    inference(substitution,[status(thm)],[c74]) ).

cnf(c178,plain,
    multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,identity),multiply(X2,identity))),identity)),identity)) = multiply(multiply(X3,X2),identity),
    inference(transitivity,[status(thm)],[c176,c177]) ).

cnf(c179,plain,
    multiply(multiply(X3,identity),multiply(X2,identity)) = multiply(multiply(X3,X2),identity),
    inference(transitivity,[status(thm)],[c169,c178]) ).

cnf(c180,plain,
    multiply(multiply(X2,identity),multiply(multiply(X2,X2),identity)) = multiply(multiply(X2,multiply(X2,X2)),identity),
    inference(substitution,[status(thm)],[c179]) ).

cnf(c181,plain,
    multiply(multiply(X2,multiply(X2,X2)),identity) = multiply(multiply(X2,identity),multiply(multiply(X2,X2),identity)),
    inference(symmetry,[status(thm)],[c180]) ).

cnf(c182,plain,
    multiply(multiply(multiply(X2,multiply(X2,X2)),identity),identity) = multiply(multiply(multiply(X2,identity),multiply(multiply(X2,X2),identity)),identity),
    inference(congruence,[status(thm)],[c181]) ).

cnf(c183,plain,
    multiply(X2,multiply(multiply(multiply(X2,multiply(X2,X2)),identity),identity)) = multiply(X2,multiply(multiply(multiply(X2,identity),multiply(multiply(X2,X2),identity)),identity)),
    inference(congruence,[status(thm)],[c182]) ).

cnf(c184,plain,
    multiply(multiply(X2,identity),multiply(X2,identity)) = multiply(multiply(X2,X2),identity),
    inference(substitution,[status(thm)],[c179]) ).

cnf(c185,plain,
    multiply(multiply(X2,X2),identity) = multiply(multiply(X2,identity),multiply(X2,identity)),
    inference(symmetry,[status(thm)],[c184]) ).

cnf(c186,plain,
    multiply(multiply(X2,identity),multiply(multiply(X2,X2),identity)) = multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))),
    inference(congruence,[status(thm)],[c185]) ).

cnf(c187,plain,
    multiply(multiply(multiply(X2,identity),multiply(multiply(X2,X2),identity)),identity) = multiply(multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))),identity),
    inference(congruence,[status(thm)],[c186]) ).

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

cnf(c189,plain,
    multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),multiply(X2,identity)),identity)) = multiply(multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))),identity),
    inference(substitution,[status(thm)],[c179]) ).

cnf(c190,plain,
    multiply(multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))),identity) = multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),multiply(X2,identity)),identity)),
    inference(symmetry,[status(thm)],[c189]) ).

cnf(c191,plain,
    multiply(X2,multiply(multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))),identity)) = multiply(X2,multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),multiply(X2,identity)),identity))),
    inference(congruence,[status(thm)],[c190]) ).

cnf(c192,plain,
    multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)) = multiply(multiply(multiply(X2,identity),multiply(X2,identity)),identity),
    inference(substitution,[status(thm)],[c179]) ).

cnf(c193,plain,
    multiply(multiply(multiply(X2,identity),multiply(X2,identity)),identity) = multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)),
    inference(symmetry,[status(thm)],[c192]) ).

cnf(c194,plain,
    multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),multiply(X2,identity)),identity)) = multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity))),
    inference(congruence,[status(thm)],[c193]) ).

cnf(c195,plain,
    multiply(X2,multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),multiply(X2,identity)),identity))) = multiply(X2,multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)))),
    inference(congruence,[status(thm)],[c194]) ).

cnf(c196,plain,
    multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(X2,multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity))))),identity),identity))) = multiply(X2,multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)))),
    inference(substitution,[status(thm)],[c98]) ).

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

cnf(c198,plain,
    X2 = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X2,identity),identity)))),
    inference(symmetry,[status(thm)],[c44]) ).

cnf(c199,plain,
    multiply(X2,multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)))) = multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X2,identity),identity)))),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)))),
    inference(congruence,[status(thm)],[c198]) ).

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

cnf(c201,plain,
    multiply(identity,multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X2,identity),identity)))),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity))))) = identity,
    inference(substitution,[status(thm)],[c83]) ).

cnf(c202,plain,
    multiply(identity,multiply(X2,multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity))))) = identity,
    inference(transitivity,[status(thm)],[c200,c201]) ).

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

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

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

cnf(c206,plain,
    multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(X2,multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity))))),identity),identity))) = multiply(identity,multiply(identity,multiply(multiply(identity,identity),identity))),
    inference(congruence,[status(thm)],[c205]) ).

cnf(c207,plain,
    multiply(identity,multiply(multiply(identity,identity),identity)) = multiply(identity,multiply(identity,multiply(identity,identity))),
    inference(substitution,[status(thm)],[c30]) ).

cnf(c208,plain,
    multiply(identity,multiply(identity,multiply(multiply(identity,identity),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(identity,identity)))),
    inference(congruence,[status(thm)],[c207]) ).

cnf(c209,plain,
    multiply(identity,multiply(identity,identity)) = multiply(identity,identity),
    inference(congruence,[status(thm)],[c2]) ).

cnf(c210,plain,
    multiply(identity,multiply(identity,multiply(identity,identity))) = multiply(identity,multiply(identity,identity)),
    inference(congruence,[status(thm)],[c209]) ).

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

cnf(c212,plain,
    multiply(identity,multiply(identity,identity)) = multiply(identity,identity),
    inference(congruence,[status(thm)],[c2]) ).

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

cnf(c214,plain,
    multiply(identity,multiply(identity,identity)) = multiply(identity,identity),
    inference(congruence,[status(thm)],[c2]) ).

cnf(c215,plain,
    multiply(identity,multiply(identity,identity)) = identity,
    inference(transitivity,[status(thm)],[c214,c2]) ).

cnf(c216,plain,
    multiply(identity,multiply(identity,multiply(identity,identity))) = identity,
    inference(transitivity,[status(thm)],[c213,c215]) ).

cnf(c217,plain,
    multiply(identity,multiply(identity,multiply(identity,multiply(identity,identity)))) = identity,
    inference(transitivity,[status(thm)],[c211,c216]) ).

cnf(c218,plain,
    multiply(identity,multiply(identity,multiply(multiply(identity,identity),identity))) = identity,
    inference(transitivity,[status(thm)],[c208,c217]) ).

cnf(c219,plain,
    multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(X2,multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity))))),identity),identity))) = identity,
    inference(transitivity,[status(thm)],[c206,c218]) ).

cnf(c220,plain,
    multiply(X2,multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)))) = identity,
    inference(transitivity,[status(thm)],[c197,c219]) ).

cnf(c221,plain,
    multiply(X2,multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),multiply(X2,identity)),identity))) = identity,
    inference(transitivity,[status(thm)],[c195,c220]) ).

cnf(c222,plain,
    multiply(X2,multiply(multiply(multiply(X2,identity),multiply(multiply(X2,identity),multiply(X2,identity))),identity)) = identity,
    inference(transitivity,[status(thm)],[c191,c221]) ).

cnf(c223,plain,
    multiply(X2,multiply(multiply(multiply(X2,identity),multiply(multiply(X2,X2),identity)),identity)) = identity,
    inference(transitivity,[status(thm)],[c188,c222]) ).

cnf(c224,plain,
    multiply(X2,multiply(multiply(multiply(X2,multiply(X2,X2)),identity),identity)) = identity,
    inference(transitivity,[status(thm)],[c183,c223]) ).

cnf(c225,plain,
    multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))),identity),identity)) = identity,
    inference(substitution,[status(thm)],[c224]) ).

cnf(c226,plain,
    multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(multiply(identity,X2),identity),identity)) = identity,
    inference(transitivity,[status(thm)],[c167,c225]) ).

cnf(c227,plain,
    multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(identity,multiply(X2,identity)),identity)) = identity,
    inference(transitivity,[status(thm)],[c163,c226]) ).

cnf(c228,plain,
    multiply(multiply(X2,multiply(X2,X2)),multiply(identity,multiply(multiply(X2,identity),identity))) = identity,
    inference(transitivity,[status(thm)],[c160,c227]) ).

cnf(c229,plain,
    multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity))) = identity,
    inference(transitivity,[status(thm)],[c152,c228]) ).

cnf(c230,plain,
    identity = multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity))),
    inference(symmetry,[status(thm)],[c229]) ).

cnf(c231,plain,
    multiply(multiply(X2,X2),identity) = multiply(multiply(X2,X2),multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity)))),
    inference(congruence,[status(thm)],[c230]) ).

cnf(c232,plain,
    multiply(multiply(multiply(X2,X2),identity),identity) = multiply(multiply(multiply(X2,X2),multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity)))),identity),
    inference(congruence,[status(thm)],[c231]) ).

cnf(c233,plain,
    multiply(multiply(multiply(multiply(X2,X2),identity),identity),identity) = multiply(multiply(multiply(multiply(X2,X2),multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity)))),identity),identity),
    inference(congruence,[status(thm)],[c232]) ).

cnf(c234,plain,
    multiply(multiply(multiply(X2,X2),identity),multiply(multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity))),identity)) = multiply(multiply(multiply(X2,X2),multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity)))),identity),
    inference(substitution,[status(thm)],[c179]) ).

cnf(c235,plain,
    multiply(multiply(multiply(X2,X2),multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity)))),identity) = multiply(multiply(multiply(X2,X2),identity),multiply(multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity))),identity)),
    inference(symmetry,[status(thm)],[c234]) ).

cnf(c236,plain,
    multiply(multiply(multiply(multiply(X2,X2),multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity)))),identity),identity) = multiply(multiply(multiply(multiply(X2,X2),identity),multiply(multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity))),identity)),identity),
    inference(congruence,[status(thm)],[c235]) ).

cnf(c237,plain,
    multiply(multiply(X2,identity),multiply(X2,identity)) = multiply(multiply(X2,X2),identity),
    inference(substitution,[status(thm)],[c179]) ).

cnf(c238,plain,
    multiply(multiply(X2,X2),identity) = multiply(multiply(X2,identity),multiply(X2,identity)),
    inference(symmetry,[status(thm)],[c237]) ).

cnf(c239,plain,
    multiply(multiply(multiply(X2,X2),identity),multiply(multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity))),identity)) = multiply(multiply(multiply(X2,identity),multiply(X2,identity)),multiply(multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity))),identity)),
    inference(congruence,[status(thm)],[c238]) ).

cnf(c240,plain,
    multiply(multiply(multiply(multiply(X2,X2),identity),multiply(multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity))),identity)),identity) = multiply(multiply(multiply(multiply(X2,identity),multiply(X2,identity)),multiply(multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity))),identity)),identity),
    inference(congruence,[status(thm)],[c239]) ).

cnf(c241,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(X2,multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)))),identity)),identity)) = multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity))),
    inference(substitution,[status(thm)],[c74]) ).

cnf(c242,plain,
    multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity))) = multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(X2,multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)))),identity)),identity)),
    inference(symmetry,[status(thm)],[c241]) ).

cnf(c243,plain,
    multiply(multiply(X2,multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)))),identity) = multiply(identity,identity),
    inference(congruence,[status(thm)],[c220]) ).

cnf(c244,plain,
    multiply(X2,multiply(multiply(X2,multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)))),identity)) = multiply(X2,multiply(identity,identity)),
    inference(congruence,[status(thm)],[c243]) ).

cnf(c245,plain,
    multiply(multiply(X2,multiply(multiply(X2,multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)))),identity)),identity) = multiply(multiply(X2,multiply(identity,identity)),identity),
    inference(congruence,[status(thm)],[c244]) ).

cnf(c246,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(X2,multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)))),identity)),identity)) = multiply(multiply(X2,X2),multiply(multiply(X2,multiply(identity,identity)),identity)),
    inference(congruence,[status(thm)],[c245]) ).

cnf(c247,plain,
    multiply(X2,multiply(identity,identity)) = multiply(X2,identity),
    inference(congruence,[status(thm)],[c2]) ).

cnf(c248,plain,
    multiply(multiply(X2,multiply(identity,identity)),identity) = multiply(multiply(X2,identity),identity),
    inference(congruence,[status(thm)],[c247]) ).

cnf(c249,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,multiply(identity,identity)),identity)) = multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity)),
    inference(congruence,[status(thm)],[c248]) ).

cnf(c250,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(X2,multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)))),identity)),identity)) = multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity)),
    inference(transitivity,[status(thm)],[c246,c249]) ).

cnf(c251,plain,
    multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity))) = multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity)),
    inference(transitivity,[status(thm)],[c242,c250]) ).

cnf(c252,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity)) = multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity))),
    inference(symmetry,[status(thm)],[c251]) ).

cnf(c253,plain,
    multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity))) = multiply(multiply(X2,identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)))),
    inference(congruence,[status(thm)],[c252]) ).

cnf(c254,plain,
    multiply(multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity))),identity) = multiply(multiply(multiply(X2,identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)))),identity),
    inference(congruence,[status(thm)],[c253]) ).

cnf(c255,plain,
    multiply(multiply(multiply(X2,identity),multiply(X2,identity)),multiply(multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity))),identity)) = multiply(multiply(multiply(X2,identity),multiply(X2,identity)),multiply(multiply(multiply(X2,identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)))),identity)),
    inference(congruence,[status(thm)],[c254]) ).

cnf(c256,plain,
    multiply(multiply(multiply(multiply(X2,identity),multiply(X2,identity)),multiply(multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity))),identity)),identity) = multiply(multiply(multiply(multiply(X2,identity),multiply(X2,identity)),multiply(multiply(multiply(X2,identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)))),identity)),identity),
    inference(congruence,[status(thm)],[c255]) ).

cnf(c257,plain,
    multiply(multiply(X3,identity),multiply(multiply(multiply(X3,identity),X2),identity)) = multiply(multiply(X3,multiply(multiply(X3,identity),X2)),identity),
    inference(substitution,[status(thm)],[c179]) ).

cnf(c258,plain,
    multiply(multiply(X3,multiply(multiply(X3,identity),X2)),identity) = multiply(multiply(X3,identity),multiply(multiply(multiply(X3,identity),X2),identity)),
    inference(symmetry,[status(thm)],[c257]) ).

cnf(c259,plain,
    multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,identity),X2)),identity)) = multiply(multiply(X3,X3),multiply(multiply(X3,identity),multiply(multiply(multiply(X3,identity),X2),identity))),
    inference(congruence,[status(thm)],[c258]) ).

cnf(c260,plain,
    multiply(multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,identity),X2)),identity)),identity) = multiply(multiply(multiply(X3,X3),multiply(multiply(X3,identity),multiply(multiply(multiply(X3,identity),X2),identity))),identity),
    inference(congruence,[status(thm)],[c259]) ).

cnf(c261,plain,
    multiply(multiply(multiply(X3,X3),identity),multiply(multiply(multiply(X3,identity),multiply(multiply(multiply(X3,identity),X2),identity)),identity)) = multiply(multiply(multiply(X3,X3),multiply(multiply(X3,identity),multiply(multiply(multiply(X3,identity),X2),identity))),identity),
    inference(substitution,[status(thm)],[c179]) ).

cnf(c262,plain,
    multiply(multiply(multiply(X3,X3),multiply(multiply(X3,identity),multiply(multiply(multiply(X3,identity),X2),identity))),identity) = multiply(multiply(multiply(X3,X3),identity),multiply(multiply(multiply(X3,identity),multiply(multiply(multiply(X3,identity),X2),identity)),identity)),
    inference(symmetry,[status(thm)],[c261]) ).

cnf(c263,plain,
    multiply(multiply(X2,identity),multiply(X2,identity)) = multiply(multiply(X2,X2),identity),
    inference(substitution,[status(thm)],[c179]) ).

cnf(c264,plain,
    multiply(multiply(X2,X2),identity) = multiply(multiply(X2,identity),multiply(X2,identity)),
    inference(symmetry,[status(thm)],[c263]) ).

cnf(c265,plain,
    multiply(multiply(multiply(X3,X3),identity),multiply(multiply(multiply(X3,identity),multiply(multiply(multiply(X3,identity),X2),identity)),identity)) = multiply(multiply(multiply(X3,identity),multiply(X3,identity)),multiply(multiply(multiply(X3,identity),multiply(multiply(multiply(X3,identity),X2),identity)),identity)),
    inference(congruence,[status(thm)],[c264]) ).

cnf(c266,plain,
    multiply(multiply(multiply(X3,identity),multiply(X3,identity)),multiply(multiply(multiply(X3,identity),multiply(multiply(multiply(X3,identity),X2),identity)),identity)) = X2,
    inference(substitution,[status(thm)],[c74]) ).

cnf(c267,plain,
    multiply(multiply(multiply(X3,X3),identity),multiply(multiply(multiply(X3,identity),multiply(multiply(multiply(X3,identity),X2),identity)),identity)) = X2,
    inference(transitivity,[status(thm)],[c265,c266]) ).

cnf(c268,plain,
    multiply(multiply(multiply(X3,X3),multiply(multiply(X3,identity),multiply(multiply(multiply(X3,identity),X2),identity))),identity) = X2,
    inference(transitivity,[status(thm)],[c262,c267]) ).

cnf(c269,plain,
    multiply(multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,identity),X2)),identity)),identity) = X2,
    inference(transitivity,[status(thm)],[c260,c268]) ).

cnf(c270,plain,
    multiply(multiply(multiply(multiply(X2,identity),multiply(X2,identity)),multiply(multiply(multiply(X2,identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)))),identity)),identity) = multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)),
    inference(substitution,[status(thm)],[c269]) ).

cnf(c271,plain,
    multiply(multiply(multiply(X4,identity),identity),multiply(multiply(X3,identity),X2)) = multiply(multiply(multiply(X4,identity),multiply(X3,identity)),multiply(identity,X2)),
    inference(substitution,[status(thm)],[c151]) ).

cnf(c272,plain,
    multiply(multiply(multiply(X4,identity),multiply(X3,identity)),multiply(identity,X2)) = multiply(multiply(multiply(X4,X3),identity),multiply(identity,X2)),
    inference(congruence,[status(thm)],[c179]) ).

cnf(c273,plain,
    multiply(multiply(multiply(X4,identity),identity),multiply(multiply(X3,identity),X2)) = multiply(multiply(multiply(X4,X3),identity),multiply(identity,X2)),
    inference(transitivity,[status(thm)],[c271,c272]) ).

cnf(c274,plain,
    multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)) = multiply(multiply(multiply(X2,X2),identity),multiply(identity,identity)),
    inference(substitution,[status(thm)],[c273]) ).

cnf(c275,plain,
    multiply(multiply(multiply(X2,X2),identity),multiply(identity,identity)) = multiply(multiply(multiply(X2,X2),identity),identity),
    inference(substitution,[status(thm)],[c179]) ).

cnf(c276,plain,
    multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)) = multiply(multiply(multiply(X2,X2),identity),identity),
    inference(transitivity,[status(thm)],[c274,c275]) ).

cnf(c277,plain,
    multiply(multiply(multiply(multiply(X2,identity),multiply(X2,identity)),multiply(multiply(multiply(X2,identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(multiply(X2,identity),identity),multiply(multiply(X2,identity),identity)))),identity)),identity) = multiply(multiply(multiply(X2,X2),identity),identity),
    inference(transitivity,[status(thm)],[c270,c276]) ).

cnf(c278,plain,
    multiply(multiply(multiply(multiply(X2,identity),multiply(X2,identity)),multiply(multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity))),identity)),identity) = multiply(multiply(multiply(X2,X2),identity),identity),
    inference(transitivity,[status(thm)],[c256,c277]) ).

cnf(c279,plain,
    multiply(multiply(multiply(multiply(X2,X2),identity),multiply(multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity))),identity)),identity) = multiply(multiply(multiply(X2,X2),identity),identity),
    inference(transitivity,[status(thm)],[c240,c278]) ).

cnf(c280,plain,
    multiply(multiply(multiply(multiply(X2,X2),multiply(multiply(X2,identity),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity)))),identity),identity) = multiply(multiply(multiply(X2,X2),identity),identity),
    inference(transitivity,[status(thm)],[c236,c279]) ).

cnf(c281,plain,
    multiply(multiply(multiply(multiply(X2,X2),identity),identity),identity) = multiply(multiply(multiply(X2,X2),identity),identity),
    inference(transitivity,[status(thm)],[c233,c280]) ).

cnf(c282,plain,
    multiply(identity,multiply(multiply(multiply(multiply(X2,X2),identity),identity),identity)) = multiply(identity,multiply(multiply(multiply(X2,X2),identity),identity)),
    inference(congruence,[status(thm)],[c281]) ).

cnf(c283,plain,
    multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(X2,X2),identity),identity),identity))) = multiply(identity,multiply(identity,multiply(multiply(multiply(X2,X2),identity),identity))),
    inference(congruence,[status(thm)],[c282]) ).

cnf(c284,plain,
    multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(X2,X2),identity),identity),identity)))) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(X2,X2),identity),identity)))),
    inference(congruence,[status(thm)],[c283]) ).

cnf(c285,plain,
    multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(X2,X2),identity),identity)))) = multiply(X2,X2),
    inference(substitution,[status(thm)],[c44]) ).

cnf(c286,plain,
    multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(X2,X2),identity),identity),identity)))) = multiply(X2,X2),
    inference(transitivity,[status(thm)],[c284,c285]) ).

cnf(c287,plain,
    multiply(multiply(X2,X2),identity) = multiply(X2,X2),
    inference(transitivity,[status(thm)],[c46,c286]) ).

cnf(c288,plain,
    multiply(X2,X2) = multiply(multiply(X2,X2),identity),
    inference(symmetry,[status(thm)],[c287]) ).

cnf(c289,plain,
    multiply(X2,multiply(X2,X2)) = multiply(X2,multiply(multiply(X2,X2),identity)),
    inference(congruence,[status(thm)],[c288]) ).

cnf(c290,plain,
    multiply(multiply(X2,X2),multiply(X2,multiply(X2,X2))) = multiply(multiply(X2,X2),multiply(X2,multiply(multiply(X2,X2),identity))),
    inference(congruence,[status(thm)],[c289]) ).

cnf(c291,plain,
    multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),identity)),identity)),identity)) = multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),identity),
    inference(substitution,[status(thm)],[c74]) ).

cnf(c292,plain,
    multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),identity) = multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),identity)),identity)),identity)),
    inference(symmetry,[status(thm)],[c291]) ).

cnf(c293,plain,
    multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),identity)),identity) = multiply(X2,identity),
    inference(congruence,[status(thm)],[c13]) ).

cnf(c294,plain,
    multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),identity)),identity)) = multiply(X3,multiply(X2,identity)),
    inference(congruence,[status(thm)],[c293]) ).

cnf(c295,plain,
    multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),identity)),identity)),identity) = multiply(multiply(X3,multiply(X2,identity)),identity),
    inference(congruence,[status(thm)],[c294]) ).

cnf(c296,plain,
    multiply(multiply(X3,X3),multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),identity)),identity)),identity)) = multiply(multiply(X3,X3),multiply(multiply(X3,multiply(X2,identity)),identity)),
    inference(congruence,[status(thm)],[c295]) ).

cnf(c297,plain,
    multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),identity) = multiply(multiply(X3,X3),multiply(multiply(X3,multiply(X2,identity)),identity)),
    inference(transitivity,[status(thm)],[c292,c296]) ).

cnf(c298,plain,
    multiply(multiply(X3,X3),multiply(multiply(X3,multiply(X2,identity)),identity)) = multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),identity),
    inference(symmetry,[status(thm)],[c297]) ).

cnf(c299,plain,
    multiply(X3,multiply(multiply(X3,X3),multiply(multiply(X3,multiply(X2,identity)),identity))) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X3),multiply(X2,identity))),identity)),
    inference(congruence,[status(thm)],[c298]) ).

cnf(c300,plain,
    multiply(X3,multiply(multiply(X3,X3),multiply(multiply(X3,multiply(X2,identity)),identity))) = X2,
    inference(transitivity,[status(thm)],[c299,c13]) ).

cnf(c301,plain,
    multiply(X2,multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(multiply(X2,multiply(X2,X2)),identity),identity)),identity))) = multiply(multiply(X2,multiply(X2,X2)),identity),
    inference(substitution,[status(thm)],[c300]) ).

cnf(c302,plain,
    multiply(multiply(X2,multiply(X2,X2)),identity) = multiply(X2,multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(multiply(X2,multiply(X2,X2)),identity),identity)),identity))),
    inference(symmetry,[status(thm)],[c301]) ).

cnf(c303,plain,
    multiply(multiply(X2,multiply(multiply(multiply(X2,multiply(X2,X2)),identity),identity)),identity) = multiply(identity,identity),
    inference(congruence,[status(thm)],[c224]) ).

cnf(c304,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(multiply(X2,multiply(X2,X2)),identity),identity)),identity)) = multiply(multiply(X2,X2),multiply(identity,identity)),
    inference(congruence,[status(thm)],[c303]) ).

cnf(c305,plain,
    multiply(X2,multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(multiply(X2,multiply(X2,X2)),identity),identity)),identity))) = multiply(X2,multiply(multiply(X2,X2),multiply(identity,identity))),
    inference(congruence,[status(thm)],[c304]) ).

cnf(c306,plain,
    multiply(multiply(X2,X2),multiply(identity,identity)) = multiply(multiply(X2,X2),identity),
    inference(congruence,[status(thm)],[c2]) ).

cnf(c307,plain,
    multiply(X2,multiply(multiply(X2,X2),multiply(identity,identity))) = multiply(X2,multiply(multiply(X2,X2),identity)),
    inference(congruence,[status(thm)],[c306]) ).

cnf(c308,plain,
    multiply(X2,multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(multiply(X2,multiply(X2,X2)),identity),identity)),identity))) = multiply(X2,multiply(multiply(X2,X2),identity)),
    inference(transitivity,[status(thm)],[c305,c307]) ).

cnf(c309,plain,
    multiply(multiply(X2,multiply(X2,X2)),identity) = multiply(X2,multiply(multiply(X2,X2),identity)),
    inference(transitivity,[status(thm)],[c302,c308]) ).

cnf(c310,plain,
    multiply(X2,multiply(multiply(X2,X2),identity)) = multiply(multiply(X2,multiply(X2,X2)),identity),
    inference(symmetry,[status(thm)],[c309]) ).

cnf(c311,plain,
    multiply(multiply(X2,X2),multiply(X2,multiply(multiply(X2,X2),identity))) = multiply(multiply(X2,X2),multiply(multiply(X2,multiply(X2,X2)),identity)),
    inference(congruence,[status(thm)],[c310]) ).

cnf(c312,plain,
    multiply(X2,X2) = multiply(multiply(X2,X2),identity),
    inference(symmetry,[status(thm)],[c287]) ).

cnf(c313,plain,
    multiply(X2,multiply(X2,X2)) = multiply(X2,multiply(multiply(X2,X2),identity)),
    inference(congruence,[status(thm)],[c312]) ).

cnf(c314,plain,
    multiply(multiply(X2,multiply(X2,X2)),identity) = multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity),
    inference(congruence,[status(thm)],[c313]) ).

cnf(c315,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,multiply(X2,X2)),identity)) = multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity)),
    inference(congruence,[status(thm)],[c314]) ).

cnf(c316,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity)) = X2,
    inference(substitution,[status(thm)],[c74]) ).

cnf(c317,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,multiply(X2,X2)),identity)) = X2,
    inference(transitivity,[status(thm)],[c315,c316]) ).

cnf(c318,plain,
    multiply(multiply(X2,X2),multiply(X2,multiply(multiply(X2,X2),identity))) = X2,
    inference(transitivity,[status(thm)],[c311,c317]) ).

cnf(c319,plain,
    multiply(multiply(X2,X2),multiply(X2,multiply(X2,X2))) = X2,
    inference(transitivity,[status(thm)],[c290,c318]) ).

cnf(c320,plain,
    X2 = multiply(multiply(X2,X2),multiply(X2,multiply(X2,X2))),
    inference(symmetry,[status(thm)],[c319]) ).

cnf(c321,plain,
    multiply(identity,X2) = multiply(identity,multiply(multiply(X2,X2),multiply(X2,multiply(X2,X2)))),
    inference(congruence,[status(thm)],[c320]) ).

cnf(c322,plain,
    multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(X2,identity)),identity),identity))) = multiply(X2,identity),
    inference(substitution,[status(thm)],[c98]) ).

cnf(c323,plain,
    multiply(X2,identity) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(X2,identity)),identity),identity))),
    inference(symmetry,[status(thm)],[c322]) ).

cnf(c324,plain,
    multiply(multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))),identity) = multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))),identity)),
    inference(substitution,[status(thm)],[c309]) ).

cnf(c325,plain,
    multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))),identity)) = multiply(multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))),identity),
    inference(symmetry,[status(thm)],[c324]) ).

cnf(c326,plain,
    multiply(multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))),identity) = multiply(multiply(identity,X2),identity),
    inference(congruence,[status(thm)],[c132]) ).

cnf(c327,plain,
    multiply(multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))),identity) = multiply(identity,multiply(X2,identity)),
    inference(transitivity,[status(thm)],[c326,c157]) ).

cnf(c328,plain,
    multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))),identity)) = multiply(identity,multiply(X2,identity)),
    inference(transitivity,[status(thm)],[c325,c327]) ).

cnf(c329,plain,
    multiply(identity,multiply(X2,identity)) = multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))),identity)),
    inference(symmetry,[status(thm)],[c328]) ).

cnf(c330,plain,
    multiply(multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))),identity) = multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))),
    inference(substitution,[status(thm)],[c287]) ).

cnf(c331,plain,
    multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))),identity)) = multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))),
    inference(congruence,[status(thm)],[c330]) ).

cnf(c332,plain,
    multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2))),identity)) = multiply(identity,X2),
    inference(transitivity,[status(thm)],[c331,c132]) ).

cnf(c333,plain,
    multiply(identity,multiply(X2,identity)) = multiply(identity,X2),
    inference(transitivity,[status(thm)],[c329,c332]) ).

cnf(c334,plain,
    multiply(multiply(identity,multiply(X2,identity)),identity) = multiply(multiply(identity,X2),identity),
    inference(congruence,[status(thm)],[c333]) ).

cnf(c335,plain,
    multiply(multiply(multiply(identity,multiply(X2,identity)),identity),identity) = multiply(multiply(multiply(identity,X2),identity),identity),
    inference(congruence,[status(thm)],[c334]) ).

cnf(c336,plain,
    multiply(identity,multiply(multiply(multiply(identity,multiply(X2,identity)),identity),identity)) = multiply(identity,multiply(multiply(multiply(identity,X2),identity),identity)),
    inference(congruence,[status(thm)],[c335]) ).

cnf(c337,plain,
    multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(X2,identity)),identity),identity))) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X2),identity),identity))),
    inference(congruence,[status(thm)],[c336]) ).

cnf(c338,plain,
    multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(X2,identity)),identity),identity))) = X2,
    inference(transitivity,[status(thm)],[c337,c98]) ).

cnf(c339,plain,
    multiply(X2,identity) = X2,
    inference(transitivity,[status(thm)],[c323,c338]) ).

cnf(c340,plain,
    X2 = multiply(X2,identity),
    inference(symmetry,[status(thm)],[c339]) ).

cnf(c341,plain,
    multiply(X2,X2) = multiply(X2,multiply(X2,identity)),
    inference(congruence,[status(thm)],[c340]) ).

cnf(c342,plain,
    multiply(identity,multiply(X2,X2)) = multiply(identity,multiply(X2,multiply(X2,identity))),
    inference(congruence,[status(thm)],[c341]) ).

cnf(c343,plain,
    multiply(multiply(X2,identity),identity) = multiply(X2,identity),
    inference(substitution,[status(thm)],[c339]) ).

cnf(c344,plain,
    multiply(X2,identity) = multiply(multiply(X2,identity),identity),
    inference(symmetry,[status(thm)],[c343]) ).

cnf(c345,plain,
    multiply(X2,multiply(X2,identity)) = multiply(X2,multiply(multiply(X2,identity),identity)),
    inference(congruence,[status(thm)],[c344]) ).

cnf(c346,plain,
    multiply(identity,multiply(X2,multiply(X2,identity))) = multiply(identity,multiply(X2,multiply(multiply(X2,identity),identity))),
    inference(congruence,[status(thm)],[c345]) ).

cnf(c347,plain,
    multiply(identity,multiply(multiply(X2,multiply(multiply(X2,identity),identity)),identity)) = multiply(identity,multiply(X2,multiply(multiply(X2,identity),identity))),
    inference(substitution,[status(thm)],[c333]) ).

cnf(c348,plain,
    multiply(identity,multiply(X2,multiply(multiply(X2,identity),identity))) = multiply(identity,multiply(multiply(X2,multiply(multiply(X2,identity),identity)),identity)),
    inference(symmetry,[status(thm)],[c347]) ).

cnf(c349,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity)),identity)),identity)) = multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity),
    inference(substitution,[status(thm)],[c74]) ).

cnf(c350,plain,
    multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity) = multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity)),identity)),identity)),
    inference(symmetry,[status(thm)],[c349]) ).

cnf(c351,plain,
    identity = multiply(identity,identity),
    inference(symmetry,[status(thm)],[c2]) ).

cnf(c352,plain,
    multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity) = multiply(multiply(X2,multiply(multiply(X2,X2),identity)),multiply(identity,identity)),
    inference(congruence,[status(thm)],[c351]) ).

cnf(c353,plain,
    multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity)) = multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),identity)),multiply(identity,identity))),
    inference(congruence,[status(thm)],[c352]) ).

cnf(c354,plain,
    identity = multiply(identity,identity),
    inference(symmetry,[status(thm)],[c2]) ).

cnf(c355,plain,
    multiply(identity,identity) = multiply(identity,multiply(identity,identity)),
    inference(congruence,[status(thm)],[c354]) ).

cnf(c356,plain,
    multiply(multiply(X2,multiply(multiply(X2,X2),identity)),multiply(identity,identity)) = multiply(multiply(X2,multiply(multiply(X2,X2),identity)),multiply(identity,multiply(identity,identity))),
    inference(congruence,[status(thm)],[c355]) ).

cnf(c357,plain,
    multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),identity)),multiply(identity,identity))) = multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),identity)),multiply(identity,multiply(identity,identity)))),
    inference(congruence,[status(thm)],[c356]) ).

cnf(c358,plain,
    identity = multiply(identity,identity),
    inference(symmetry,[status(thm)],[c2]) ).

cnf(c359,plain,
    multiply(multiply(X2,X2),identity) = multiply(multiply(X2,X2),multiply(identity,identity)),
    inference(congruence,[status(thm)],[c358]) ).

cnf(c360,plain,
    multiply(X2,multiply(multiply(X2,X2),identity)) = multiply(X2,multiply(multiply(X2,X2),multiply(identity,identity))),
    inference(congruence,[status(thm)],[c359]) ).

cnf(c361,plain,
    multiply(multiply(X2,multiply(multiply(X2,X2),identity)),multiply(identity,multiply(identity,identity))) = multiply(multiply(X2,multiply(multiply(X2,X2),multiply(identity,identity))),multiply(identity,multiply(identity,identity))),
    inference(congruence,[status(thm)],[c360]) ).

cnf(c362,plain,
    multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),identity)),multiply(identity,multiply(identity,identity)))) = multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),multiply(identity,identity))),multiply(identity,multiply(identity,identity)))),
    inference(congruence,[status(thm)],[c361]) ).

cnf(c363,plain,
    multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),multiply(identity,identity))),multiply(identity,multiply(identity,identity)))) = identity,
    inference(substitution,[status(thm)],[c10]) ).

cnf(c364,plain,
    multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),identity)),multiply(identity,multiply(identity,identity)))) = identity,
    inference(transitivity,[status(thm)],[c362,c363]) ).

cnf(c365,plain,
    multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),identity)),multiply(identity,identity))) = identity,
    inference(transitivity,[status(thm)],[c357,c364]) ).

cnf(c366,plain,
    multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity)) = identity,
    inference(transitivity,[status(thm)],[c353,c365]) ).

cnf(c367,plain,
    multiply(multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity)),identity) = multiply(identity,identity),
    inference(congruence,[status(thm)],[c366]) ).

cnf(c368,plain,
    multiply(X2,multiply(multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity)),identity)) = multiply(X2,multiply(identity,identity)),
    inference(congruence,[status(thm)],[c367]) ).

cnf(c369,plain,
    multiply(multiply(X2,multiply(multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity)),identity)),identity) = multiply(multiply(X2,multiply(identity,identity)),identity),
    inference(congruence,[status(thm)],[c368]) ).

cnf(c370,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity)),identity)),identity)) = multiply(multiply(X2,X2),multiply(multiply(X2,multiply(identity,identity)),identity)),
    inference(congruence,[status(thm)],[c369]) ).

cnf(c371,plain,
    multiply(X2,multiply(identity,identity)) = multiply(X2,identity),
    inference(congruence,[status(thm)],[c2]) ).

cnf(c372,plain,
    multiply(multiply(X2,multiply(identity,identity)),identity) = multiply(multiply(X2,identity),identity),
    inference(congruence,[status(thm)],[c371]) ).

cnf(c373,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,multiply(identity,identity)),identity)) = multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity)),
    inference(congruence,[status(thm)],[c372]) ).

cnf(c374,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity)),identity)),identity)) = multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity)),
    inference(transitivity,[status(thm)],[c370,c373]) ).

cnf(c375,plain,
    multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity) = multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity)),
    inference(transitivity,[status(thm)],[c350,c374]) ).

cnf(c376,plain,
    multiply(multiply(multiply(X2,X2),multiply(multiply(multiply(X2,X2),multiply(X2,X2)),identity)),identity) = multiply(multiply(multiply(X2,X2),multiply(X2,X2)),multiply(multiply(multiply(X2,X2),identity),identity)),
    inference(substitution,[status(thm)],[c375]) ).

cnf(c377,plain,
    multiply(multiply(multiply(X2,X2),multiply(X2,X2)),multiply(multiply(multiply(X2,X2),identity),identity)) = multiply(multiply(multiply(X2,X2),multiply(multiply(multiply(X2,X2),multiply(X2,X2)),identity)),identity),
    inference(symmetry,[status(thm)],[c376]) ).

cnf(c378,plain,
    multiply(multiply(X2,X2),multiply(multiply(multiply(X2,X2),multiply(X2,X2)),identity)) = multiply(X2,multiply(multiply(X2,identity),identity)),
    inference(substitution,[status(thm)],[c141]) ).

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

cnf(c380,plain,
    multiply(multiply(multiply(X2,X2),multiply(X2,X2)),multiply(multiply(multiply(X2,X2),identity),identity)) = multiply(multiply(X2,multiply(multiply(X2,identity),identity)),identity),
    inference(transitivity,[status(thm)],[c377,c379]) ).

cnf(c381,plain,
    multiply(multiply(X2,multiply(multiply(X2,identity),identity)),identity) = multiply(multiply(multiply(X2,X2),multiply(X2,X2)),multiply(multiply(multiply(X2,X2),identity),identity)),
    inference(symmetry,[status(thm)],[c380]) ).

cnf(c382,plain,
    multiply(identity,multiply(multiply(X2,multiply(multiply(X2,identity),identity)),identity)) = multiply(identity,multiply(multiply(multiply(X2,X2),multiply(X2,X2)),multiply(multiply(multiply(X2,X2),identity),identity))),
    inference(congruence,[status(thm)],[c381]) ).

cnf(c383,plain,
    X2 = multiply(X2,identity),
    inference(symmetry,[status(thm)],[c339]) ).

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

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

cnf(c386,plain,
    multiply(multiply(X2,multiply(X2,identity)),identity) = multiply(X2,multiply(X2,identity)),
    inference(substitution,[status(thm)],[c339]) ).

cnf(c387,plain,
    multiply(X2,multiply(X2,identity)) = multiply(multiply(X2,multiply(X2,identity)),identity),
    inference(symmetry,[status(thm)],[c386]) ).

cnf(c388,plain,
    multiply(multiply(X2,X2),multiply(X2,multiply(X2,identity))) = multiply(multiply(X2,X2),multiply(multiply(X2,multiply(X2,identity)),identity)),
    inference(congruence,[status(thm)],[c387]) ).

cnf(c389,plain,
    X2 = multiply(X2,identity),
    inference(symmetry,[status(thm)],[c339]) ).

cnf(c390,plain,
    multiply(X2,identity) = multiply(multiply(X2,identity),identity),
    inference(congruence,[status(thm)],[c389]) ).

cnf(c391,plain,
    multiply(X2,multiply(X2,identity)) = multiply(X2,multiply(multiply(X2,identity),identity)),
    inference(congruence,[status(thm)],[c390]) ).

cnf(c392,plain,
    multiply(multiply(X2,multiply(X2,identity)),identity) = multiply(multiply(X2,multiply(multiply(X2,identity),identity)),identity),
    inference(congruence,[status(thm)],[c391]) ).

cnf(c393,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,multiply(X2,identity)),identity)) = multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(X2,identity),identity)),identity)),
    inference(congruence,[status(thm)],[c392]) ).

cnf(c394,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(X2,identity),identity)),identity)) = identity,
    inference(substitution,[status(thm)],[c74]) ).

cnf(c395,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,multiply(X2,identity)),identity)) = identity,
    inference(transitivity,[status(thm)],[c393,c394]) ).

cnf(c396,plain,
    multiply(multiply(X2,X2),multiply(X2,multiply(X2,identity))) = identity,
    inference(transitivity,[status(thm)],[c388,c395]) ).

cnf(c397,plain,
    multiply(multiply(X2,X2),multiply(X2,X2)) = identity,
    inference(transitivity,[status(thm)],[c385,c396]) ).

cnf(c398,plain,
    identity = multiply(multiply(X2,X2),multiply(X2,X2)),
    inference(symmetry,[status(thm)],[c397]) ).

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

cnf(c400,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity)) = multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity),
    inference(symmetry,[status(thm)],[c375]) ).

cnf(c401,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity))) = multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity)),
    inference(congruence,[status(thm)],[c400]) ).

cnf(c402,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity)) = X2,
    inference(substitution,[status(thm)],[c74]) ).

cnf(c403,plain,
    multiply(multiply(X2,X2),multiply(multiply(X2,X2),multiply(multiply(X2,identity),identity))) = X2,
    inference(transitivity,[status(thm)],[c401,c402]) ).

cnf(c404,plain,
    multiply(multiply(multiply(X2,X2),multiply(X2,X2)),multiply(multiply(multiply(X2,X2),multiply(X2,X2)),multiply(multiply(multiply(X2,X2),identity),identity))) = multiply(X2,X2),
    inference(substitution,[status(thm)],[c403]) ).

cnf(c405,plain,
    multiply(identity,multiply(multiply(multiply(X2,X2),multiply(X2,X2)),multiply(multiply(multiply(X2,X2),identity),identity))) = multiply(X2,X2),
    inference(transitivity,[status(thm)],[c399,c404]) ).

cnf(c406,plain,
    multiply(identity,multiply(multiply(X2,multiply(multiply(X2,identity),identity)),identity)) = multiply(X2,X2),
    inference(transitivity,[status(thm)],[c382,c405]) ).

cnf(c407,plain,
    multiply(identity,multiply(X2,multiply(multiply(X2,identity),identity))) = multiply(X2,X2),
    inference(transitivity,[status(thm)],[c348,c406]) ).

cnf(c408,plain,
    multiply(identity,multiply(X2,multiply(X2,identity))) = multiply(X2,X2),
    inference(transitivity,[status(thm)],[c346,c407]) ).

cnf(c409,plain,
    multiply(identity,multiply(X2,X2)) = multiply(X2,X2),
    inference(transitivity,[status(thm)],[c342,c408]) ).

cnf(c410,plain,
    multiply(X2,X2) = multiply(identity,multiply(X2,X2)),
    inference(symmetry,[status(thm)],[c409]) ).

cnf(c411,plain,
    multiply(multiply(X2,X2),multiply(X2,multiply(X2,X2))) = multiply(multiply(identity,multiply(X2,X2)),multiply(X2,multiply(X2,X2))),
    inference(congruence,[status(thm)],[c410]) ).

cnf(c412,plain,
    multiply(identity,multiply(multiply(X2,X2),multiply(X2,multiply(X2,X2)))) = multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))),
    inference(congruence,[status(thm)],[c411]) ).

cnf(c413,plain,
    multiply(X2,X2) = multiply(identity,multiply(X2,X2)),
    inference(symmetry,[status(thm)],[c409]) ).

cnf(c414,plain,
    multiply(identity,multiply(X2,X2)) = multiply(identity,multiply(identity,multiply(X2,X2))),
    inference(congruence,[status(thm)],[c413]) ).

cnf(c415,plain,
    multiply(multiply(identity,multiply(X2,X2)),multiply(X2,multiply(X2,X2))) = multiply(multiply(identity,multiply(identity,multiply(X2,X2))),multiply(X2,multiply(X2,X2))),
    inference(congruence,[status(thm)],[c414]) ).

cnf(c416,plain,
    multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))) = multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X2,X2))),multiply(X2,multiply(X2,X2)))),
    inference(congruence,[status(thm)],[c415]) ).

cnf(c417,plain,
    multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X2,X2))),multiply(X2,multiply(X2,X2)))) = X2,
    inference(substitution,[status(thm)],[c83]) ).

cnf(c418,plain,
    multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))) = X2,
    inference(transitivity,[status(thm)],[c416,c417]) ).

cnf(c419,plain,
    multiply(identity,multiply(multiply(X2,X2),multiply(X2,multiply(X2,X2)))) = X2,
    inference(transitivity,[status(thm)],[c412,c418]) ).

cnf(c420,plain,
    multiply(identity,X2) = X2,
    inference(transitivity,[status(thm)],[c321,c419]) ).

cnf(c421,plain,
    X2 = multiply(identity,X2),
    inference(symmetry,[status(thm)],[c420]) ).

cnf(c422,plain,
    multiply(multiply(X4,X3),X2) = multiply(multiply(X4,X3),multiply(identity,X2)),
    inference(congruence,[status(thm)],[c421]) ).

cnf(c423,plain,
    multiply(multiply(X3,X2),identity) = multiply(X3,X2),
    inference(substitution,[status(thm)],[c339]) ).

cnf(c424,plain,
    multiply(X3,X2) = multiply(multiply(X3,X2),identity),
    inference(symmetry,[status(thm)],[c423]) ).

cnf(c425,plain,
    multiply(multiply(X4,X3),multiply(identity,X2)) = multiply(multiply(multiply(X4,X3),identity),multiply(identity,X2)),
    inference(congruence,[status(thm)],[c424]) ).

cnf(c426,plain,
    multiply(X2,X2) = multiply(multiply(X2,X2),identity),
    inference(symmetry,[status(thm)],[c287]) ).

cnf(c427,plain,
    multiply(X2,multiply(X2,X2)) = multiply(X2,multiply(multiply(X2,X2),identity)),
    inference(congruence,[status(thm)],[c426]) ).

cnf(c428,plain,
    multiply(X2,multiply(X2,multiply(X2,X2))) = multiply(X2,multiply(X2,multiply(multiply(X2,X2),identity))),
    inference(congruence,[status(thm)],[c427]) ).

cnf(c429,plain,
    multiply(X2,multiply(multiply(X2,X2),identity)) = multiply(multiply(X2,multiply(X2,X2)),identity),
    inference(symmetry,[status(thm)],[c309]) ).

cnf(c430,plain,
    multiply(X2,multiply(X2,multiply(multiply(X2,X2),identity))) = multiply(X2,multiply(multiply(X2,multiply(X2,X2)),identity)),
    inference(congruence,[status(thm)],[c429]) ).

cnf(c431,plain,
    multiply(X2,X2) = multiply(multiply(X2,X2),identity),
    inference(symmetry,[status(thm)],[c287]) ).

cnf(c432,plain,
    multiply(X2,multiply(X2,X2)) = multiply(X2,multiply(multiply(X2,X2),identity)),
    inference(congruence,[status(thm)],[c431]) ).

cnf(c433,plain,
    multiply(multiply(X2,multiply(X2,X2)),identity) = multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity),
    inference(congruence,[status(thm)],[c432]) ).

cnf(c434,plain,
    multiply(X2,multiply(multiply(X2,multiply(X2,X2)),identity)) = multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X2),identity)),identity)),
    inference(congruence,[status(thm)],[c433]) ).

cnf(c435,plain,
    multiply(X2,multiply(multiply(X2,multiply(X2,X2)),identity)) = identity,
    inference(transitivity,[status(thm)],[c434,c366]) ).

cnf(c436,plain,
    multiply(X2,multiply(X2,multiply(multiply(X2,X2),identity))) = identity,
    inference(transitivity,[status(thm)],[c430,c435]) ).

cnf(c437,plain,
    multiply(X2,multiply(X2,multiply(X2,X2))) = identity,
    inference(transitivity,[status(thm)],[c428,c436]) ).

cnf(c438,plain,
    multiply(identity,multiply(identity,multiply(identity,identity))) = identity,
    inference(substitution,[status(thm)],[c437]) ).

cnf(c439,plain,
    identity = multiply(identity,multiply(identity,multiply(identity,identity))),
    inference(symmetry,[status(thm)],[c438]) ).

cnf(c440,plain,
    multiply(identity,X2) = multiply(multiply(identity,multiply(identity,multiply(identity,identity))),X2),
    inference(congruence,[status(thm)],[c439]) ).

cnf(c441,plain,
    multiply(multiply(multiply(X4,X3),identity),multiply(identity,X2)) = multiply(multiply(multiply(X4,X3),identity),multiply(multiply(identity,multiply(identity,multiply(identity,identity))),X2)),
    inference(congruence,[status(thm)],[c440]) ).

cnf(c442,plain,
    multiply(multiply(multiply(X4,identity),identity),multiply(multiply(X3,X2),X5)) = multiply(multiply(multiply(X4,identity),multiply(X3,X2)),multiply(identity,X5)),
    inference(substitution,[status(thm)],[c151]) ).

cnf(c443,plain,
    multiply(multiply(multiply(X5,identity),multiply(X4,X3)),multiply(identity,X2)) = multiply(multiply(multiply(X5,X4),multiply(identity,X3)),multiply(identity,X2)),
    inference(congruence,[status(thm)],[c151]) ).

cnf(c444,plain,
    multiply(multiply(multiply(X5,X4),identity),multiply(multiply(identity,X3),X2)) = multiply(multiply(multiply(X5,X4),multiply(identity,X3)),multiply(identity,X2)),
    inference(substitution,[status(thm)],[c151]) ).

cnf(c445,plain,
    multiply(multiply(multiply(X5,X4),multiply(identity,X3)),multiply(identity,X2)) = multiply(multiply(multiply(X5,X4),identity),multiply(multiply(identity,X3),X2)),
    inference(symmetry,[status(thm)],[c444]) ).

cnf(c446,plain,
    multiply(multiply(multiply(X5,identity),multiply(X4,X3)),multiply(identity,X2)) = multiply(multiply(multiply(X5,X4),identity),multiply(multiply(identity,X3),X2)),
    inference(transitivity,[status(thm)],[c443,c445]) ).

cnf(c447,plain,
    multiply(multiply(multiply(X5,identity),identity),multiply(multiply(X4,X3),X2)) = multiply(multiply(multiply(X5,X4),identity),multiply(multiply(identity,X3),X2)),
    inference(transitivity,[status(thm)],[c442,c446]) ).

cnf(c448,plain,
    multiply(multiply(multiply(X4,identity),identity),multiply(multiply(X3,multiply(identity,multiply(identity,identity))),X2)) = multiply(multiply(multiply(X4,X3),identity),multiply(multiply(identity,multiply(identity,multiply(identity,identity))),X2)),
    inference(substitution,[status(thm)],[c447]) ).

cnf(c449,plain,
    multiply(multiply(multiply(X4,X3),identity),multiply(multiply(identity,multiply(identity,multiply(identity,identity))),X2)) = multiply(multiply(multiply(X4,identity),identity),multiply(multiply(X3,multiply(identity,multiply(identity,identity))),X2)),
    inference(symmetry,[status(thm)],[c448]) ).

cnf(c450,plain,
    multiply(multiply(X2,identity),identity) = multiply(X2,identity),
    inference(substitution,[status(thm)],[c339]) ).

cnf(c451,plain,
    multiply(multiply(multiply(X4,identity),identity),multiply(multiply(X3,multiply(identity,multiply(identity,identity))),X2)) = multiply(multiply(X4,identity),multiply(multiply(X3,multiply(identity,multiply(identity,identity))),X2)),
    inference(congruence,[status(thm)],[c450]) ).

cnf(c452,plain,
    multiply(multiply(X4,identity),multiply(multiply(X3,multiply(identity,multiply(identity,identity))),X2)) = multiply(X4,multiply(multiply(X3,multiply(identity,multiply(identity,identity))),X2)),
    inference(congruence,[status(thm)],[c339]) ).

cnf(c453,plain,
    multiply(identity,multiply(identity,identity)) = multiply(identity,identity),
    inference(substitution,[status(thm)],[c333]) ).

cnf(c454,plain,
    multiply(X2,multiply(identity,multiply(identity,identity))) = multiply(X2,multiply(identity,identity)),
    inference(congruence,[status(thm)],[c453]) ).

cnf(c455,plain,
    multiply(multiply(X3,multiply(identity,multiply(identity,identity))),X2) = multiply(multiply(X3,multiply(identity,identity)),X2),
    inference(congruence,[status(thm)],[c454]) ).

cnf(c456,plain,
    multiply(X4,multiply(multiply(X3,multiply(identity,multiply(identity,identity))),X2)) = multiply(X4,multiply(multiply(X3,multiply(identity,identity)),X2)),
    inference(congruence,[status(thm)],[c455]) ).

cnf(c457,plain,
    multiply(X2,multiply(identity,identity)) = multiply(X2,identity),
    inference(congruence,[status(thm)],[c2]) ).

cnf(c458,plain,
    multiply(multiply(X3,multiply(identity,identity)),X2) = multiply(multiply(X3,identity),X2),
    inference(congruence,[status(thm)],[c457]) ).

cnf(c459,plain,
    multiply(X4,multiply(multiply(X3,multiply(identity,identity)),X2)) = multiply(X4,multiply(multiply(X3,identity),X2)),
    inference(congruence,[status(thm)],[c458]) ).

cnf(c460,plain,
    multiply(multiply(X3,identity),X2) = multiply(X3,X2),
    inference(congruence,[status(thm)],[c339]) ).

cnf(c461,plain,
    multiply(X4,multiply(multiply(X3,identity),X2)) = multiply(X4,multiply(X3,X2)),
    inference(congruence,[status(thm)],[c460]) ).

cnf(c462,plain,
    multiply(X4,multiply(multiply(X3,multiply(identity,identity)),X2)) = multiply(X4,multiply(X3,X2)),
    inference(transitivity,[status(thm)],[c459,c461]) ).

cnf(c463,plain,
    multiply(X4,multiply(multiply(X3,multiply(identity,multiply(identity,identity))),X2)) = multiply(X4,multiply(X3,X2)),
    inference(transitivity,[status(thm)],[c456,c462]) ).

cnf(c464,plain,
    multiply(multiply(X4,identity),multiply(multiply(X3,multiply(identity,multiply(identity,identity))),X2)) = multiply(X4,multiply(X3,X2)),
    inference(transitivity,[status(thm)],[c452,c463]) ).

cnf(c465,plain,
    multiply(multiply(multiply(X4,identity),identity),multiply(multiply(X3,multiply(identity,multiply(identity,identity))),X2)) = multiply(X4,multiply(X3,X2)),
    inference(transitivity,[status(thm)],[c451,c464]) ).

cnf(c466,plain,
    multiply(multiply(multiply(X4,X3),identity),multiply(multiply(identity,multiply(identity,multiply(identity,identity))),X2)) = multiply(X4,multiply(X3,X2)),
    inference(transitivity,[status(thm)],[c449,c465]) ).

cnf(c467,plain,
    multiply(multiply(multiply(X4,X3),identity),multiply(identity,X2)) = multiply(X4,multiply(X3,X2)),
    inference(transitivity,[status(thm)],[c441,c466]) ).

cnf(c468,plain,
    multiply(multiply(X4,X3),multiply(identity,X2)) = multiply(X4,multiply(X3,X2)),
    inference(transitivity,[status(thm)],[c425,c467]) ).

cnf(c469,plain,
    multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X3,X2)),
    inference(transitivity,[status(thm)],[c422,c468]) ).

cnf(c470,plain,
    multiply(multiply(a,b),c) = multiply(a,multiply(b,c)),
    inference(substitution,[status(thm)],[c469]) ).

cnf(c471,plain,
    $false,
    inference(resolution,[status(thm)],[c1,c470]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : GRP122-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36  % Computer : n013.cluster.edu
% 0.09/0.36  % Model    : x86_64 x86_64
% 0.09/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36  % Memory   : 8046.5625MB
% 0.09/0.36  % OS       : Linux 6.8.0-71-generic
% 0.09/0.36  % CPULimit : 300
% 0.09/0.36  % WCLimit  : 300
% 0.09/0.36  % DateTime : Sun Sep 27 09:19:21 UTC 2026
% 0.09/0.36  % CPUTime  : 
% 0.09/0.36  Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.78/0.61  Command-line arguments: --no-flatten-goal
% 0.78/0.61  
% 0.78/0.61  % SZS status Unsatisfiable
% 0.78/0.61  
% 1.63/0.65  % SZS output start CNFRefutation
% See solution above
% 3.33/0.95  
% 3.33/0.95  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------