Twee---2.7.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : GRP024-5 : TPTP v9.3.1. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 10:09:05 AM UTC 2026

% Result   : Unsatisfiable 144.57s 18.64s
% Output   : CNFRefutation 147.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :  104
%            Number of leaves      :    6
% Syntax   : Number of clauses     :  672 ( 672 unt;   0 nHn;   5 RR)
%            Number of literals    :  672 ( 671 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   : 1620 (  36 sgn)

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

cnf(c2,axiom,
    multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).

cnf(c3,plain,
    multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
    inference(substitution,[status(thm)],[c2]) ).

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

cnf(c5,axiom,
    multiply(inverse(X2),X2) = identity,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).

cnf(c6,plain,
    multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
    inference(congruence,[status(thm)],[c5]) ).

cnf(c7,axiom,
    multiply(identity,X2) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).

cnf(c8,plain,
    multiply(multiply(inverse(X3),X3),X2) = X2,
    inference(transitivity,[status(thm)],[c6,c7]) ).

cnf(c9,plain,
    multiply(inverse(X3),multiply(X3,X2)) = X2,
    inference(transitivity,[status(thm)],[c4,c8]) ).

cnf(c10,plain,
    X2 = multiply(inverse(X3),multiply(X3,X2)),
    inference(symmetry,[status(thm)],[c9]) ).

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

cnf(c12,plain,
    multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
    inference(substitution,[status(thm)],[c9]) ).

cnf(c13,plain,
    multiply(inverse(inverse(X3)),X2) = multiply(X3,X2),
    inference(transitivity,[status(thm)],[c11,c12]) ).

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

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

cnf(c16,plain,
    identity = multiply(inverse(X2),X2),
    inference(symmetry,[status(thm)],[c5]) ).

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

cnf(c18,plain,
    multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)) = X2,
    inference(substitution,[status(thm)],[c9]) ).

cnf(c19,plain,
    multiply(inverse(inverse(X2)),identity) = X2,
    inference(transitivity,[status(thm)],[c17,c18]) ).

cnf(c20,plain,
    multiply(X2,identity) = X2,
    inference(transitivity,[status(thm)],[c15,c19]) ).

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

cnf(c22,plain,
    multiply(commutator(X2,X4),X3) = multiply(commutator(X2,X4),multiply(X3,identity)),
    inference(congruence,[status(thm)],[c21]) ).

cnf(c23,plain,
    multiply(inverse(inverse(X3)),multiply(inverse(X3),X2)) = multiply(X3,multiply(inverse(X3),X2)),
    inference(substitution,[status(thm)],[c13]) ).

cnf(c24,plain,
    multiply(X3,multiply(inverse(X3),X2)) = multiply(inverse(inverse(X3)),multiply(inverse(X3),X2)),
    inference(symmetry,[status(thm)],[c23]) ).

cnf(c25,plain,
    multiply(inverse(inverse(X3)),multiply(inverse(X3),X2)) = X2,
    inference(substitution,[status(thm)],[c9]) ).

cnf(c26,plain,
    multiply(X3,multiply(inverse(X3),X2)) = X2,
    inference(transitivity,[status(thm)],[c24,c25]) ).

cnf(c27,plain,
    multiply(X2,multiply(inverse(X2),commutator(X4,commutator(X3,X2)))) = commutator(X4,commutator(X3,X2)),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c28,plain,
    commutator(X4,commutator(X3,X2)) = multiply(X2,multiply(inverse(X2),commutator(X4,commutator(X3,X2)))),
    inference(symmetry,[status(thm)],[c27]) ).

cnf(c29,hypothesis,
    commutator(commutator(X2,Y2),Z2) = commutator(X2,commutator(Y2,Z2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_commutator) ).

cnf(c30,plain,
    commutator(commutator(X4,X3),inverse(X2)) = commutator(X4,commutator(X3,inverse(X2))),
    inference(substitution,[status(thm)],[c29]) ).

cnf(c31,plain,
    commutator(X4,commutator(X3,inverse(X2))) = commutator(commutator(X4,X3),inverse(X2)),
    inference(symmetry,[status(thm)],[c30]) ).

cnf(c32,plain,
    multiply(inverse(inverse(X3)),multiply(inverse(X2),multiply(inverse(X3),X2))) = multiply(X3,multiply(inverse(X2),multiply(inverse(X3),X2))),
    inference(substitution,[status(thm)],[c13]) ).

cnf(c33,plain,
    multiply(X3,multiply(inverse(X2),multiply(inverse(X3),X2))) = multiply(inverse(inverse(X3)),multiply(inverse(X2),multiply(inverse(X3),X2))),
    inference(symmetry,[status(thm)],[c32]) ).

cnf(c34,axiom,
    commutator(X2,Y2) = multiply(inverse(X2),multiply(inverse(Y2),multiply(X2,Y2))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',name) ).

cnf(c35,plain,
    commutator(inverse(X3),X2) = multiply(inverse(inverse(X3)),multiply(inverse(X2),multiply(inverse(X3),X2))),
    inference(substitution,[status(thm)],[c34]) ).

cnf(c36,plain,
    multiply(inverse(inverse(X3)),multiply(inverse(X2),multiply(inverse(X3),X2))) = commutator(inverse(X3),X2),
    inference(symmetry,[status(thm)],[c35]) ).

cnf(c37,plain,
    multiply(X3,multiply(inverse(X2),multiply(inverse(X3),X2))) = commutator(inverse(X3),X2),
    inference(transitivity,[status(thm)],[c33,c36]) ).

cnf(c38,plain,
    multiply(X3,multiply(inverse(multiply(X3,X2)),multiply(inverse(X3),multiply(X3,X2)))) = commutator(inverse(X3),multiply(X3,X2)),
    inference(substitution,[status(thm)],[c37]) ).

cnf(c39,plain,
    commutator(inverse(X3),multiply(X3,X2)) = multiply(X3,multiply(inverse(multiply(X3,X2)),multiply(inverse(X3),multiply(X3,X2)))),
    inference(symmetry,[status(thm)],[c38]) ).

cnf(c40,plain,
    multiply(inverse(multiply(X3,X2)),multiply(inverse(X3),multiply(X3,X2))) = multiply(inverse(multiply(X3,X2)),X2),
    inference(congruence,[status(thm)],[c9]) ).

cnf(c41,plain,
    multiply(X3,multiply(inverse(multiply(X3,X2)),multiply(inverse(X3),multiply(X3,X2)))) = multiply(X3,multiply(inverse(multiply(X3,X2)),X2)),
    inference(congruence,[status(thm)],[c40]) ).

cnf(c42,plain,
    multiply(inverse(X2),multiply(X2,inverse(multiply(X3,X2)))) = inverse(multiply(X3,X2)),
    inference(substitution,[status(thm)],[c9]) ).

cnf(c43,plain,
    inverse(multiply(X3,X2)) = multiply(inverse(X2),multiply(X2,inverse(multiply(X3,X2)))),
    inference(symmetry,[status(thm)],[c42]) ).

cnf(c44,plain,
    multiply(inverse(X2),multiply(X2,multiply(X3,inverse(multiply(X2,X3))))) = multiply(X3,inverse(multiply(X2,X3))),
    inference(substitution,[status(thm)],[c9]) ).

cnf(c45,plain,
    multiply(X3,inverse(multiply(X2,X3))) = multiply(inverse(X2),multiply(X2,multiply(X3,inverse(multiply(X2,X3))))),
    inference(symmetry,[status(thm)],[c44]) ).

cnf(c46,plain,
    multiply(multiply(X3,X2),inverse(multiply(X3,X2))) = multiply(X3,multiply(X2,inverse(multiply(X3,X2)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c47,plain,
    multiply(X3,multiply(X2,inverse(multiply(X3,X2)))) = multiply(multiply(X3,X2),inverse(multiply(X3,X2))),
    inference(symmetry,[status(thm)],[c46]) ).

cnf(c48,plain,
    multiply(inverse(inverse(X2)),inverse(X2)) = multiply(X2,inverse(X2)),
    inference(substitution,[status(thm)],[c13]) ).

cnf(c49,plain,
    multiply(X2,inverse(X2)) = multiply(inverse(inverse(X2)),inverse(X2)),
    inference(symmetry,[status(thm)],[c48]) ).

cnf(c50,plain,
    multiply(inverse(inverse(X2)),inverse(X2)) = identity,
    inference(substitution,[status(thm)],[c5]) ).

cnf(c51,plain,
    multiply(X2,inverse(X2)) = identity,
    inference(transitivity,[status(thm)],[c49,c50]) ).

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

cnf(c53,plain,
    multiply(X3,multiply(X2,inverse(multiply(X3,X2)))) = identity,
    inference(transitivity,[status(thm)],[c47,c52]) ).

cnf(c54,plain,
    multiply(X2,multiply(X3,inverse(multiply(X2,X3)))) = identity,
    inference(substitution,[status(thm)],[c53]) ).

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

cnf(c56,plain,
    multiply(inverse(X2),identity) = inverse(X2),
    inference(substitution,[status(thm)],[c20]) ).

cnf(c57,plain,
    multiply(inverse(X2),multiply(X2,multiply(X3,inverse(multiply(X2,X3))))) = inverse(X2),
    inference(transitivity,[status(thm)],[c55,c56]) ).

cnf(c58,plain,
    multiply(X3,inverse(multiply(X2,X3))) = inverse(X2),
    inference(transitivity,[status(thm)],[c45,c57]) ).

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

cnf(c60,plain,
    multiply(inverse(X2),multiply(X2,inverse(multiply(X3,X2)))) = multiply(inverse(X2),inverse(X3)),
    inference(congruence,[status(thm)],[c59]) ).

cnf(c61,plain,
    inverse(multiply(X3,X2)) = multiply(inverse(X2),inverse(X3)),
    inference(transitivity,[status(thm)],[c43,c60]) ).

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

cnf(c63,plain,
    multiply(X3,multiply(inverse(multiply(X3,X2)),X2)) = multiply(X3,multiply(multiply(inverse(X2),inverse(X3)),X2)),
    inference(congruence,[status(thm)],[c62]) ).

cnf(c64,plain,
    multiply(multiply(inverse(X2),inverse(X3)),X2) = multiply(inverse(X2),multiply(inverse(X3),X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c65,plain,
    multiply(X3,multiply(multiply(inverse(X2),inverse(X3)),X2)) = multiply(X3,multiply(inverse(X2),multiply(inverse(X3),X2))),
    inference(congruence,[status(thm)],[c64]) ).

cnf(c66,plain,
    multiply(X3,multiply(multiply(inverse(X2),inverse(X3)),X2)) = commutator(inverse(X3),X2),
    inference(transitivity,[status(thm)],[c65,c37]) ).

cnf(c67,plain,
    multiply(X3,multiply(inverse(multiply(X3,X2)),X2)) = commutator(inverse(X3),X2),
    inference(transitivity,[status(thm)],[c63,c66]) ).

cnf(c68,plain,
    multiply(X3,multiply(inverse(multiply(X3,X2)),multiply(inverse(X3),multiply(X3,X2)))) = commutator(inverse(X3),X2),
    inference(transitivity,[status(thm)],[c41,c67]) ).

cnf(c69,plain,
    commutator(inverse(X3),multiply(X3,X2)) = commutator(inverse(X3),X2),
    inference(transitivity,[status(thm)],[c39,c68]) ).

cnf(c70,plain,
    commutator(inverse(X3),X2) = commutator(inverse(X3),multiply(X3,X2)),
    inference(symmetry,[status(thm)],[c69]) ).

cnf(c71,plain,
    commutator(X3,X2) = multiply(inverse(X3),multiply(inverse(X2),multiply(X3,X2))),
    inference(substitution,[status(thm)],[c34]) ).

cnf(c72,plain,
    inverse(commutator(X3,X2)) = inverse(multiply(inverse(X3),multiply(inverse(X2),multiply(X3,X2)))),
    inference(congruence,[status(thm)],[c71]) ).

cnf(c73,plain,
    inverse(multiply(inverse(X3),multiply(inverse(X2),multiply(X3,X2)))) = multiply(inverse(multiply(inverse(X2),multiply(X3,X2))),inverse(inverse(X3))),
    inference(substitution,[status(thm)],[c61]) ).

cnf(c74,plain,
    inverse(multiply(inverse(X2),multiply(X3,X2))) = multiply(inverse(multiply(X3,X2)),inverse(inverse(X2))),
    inference(substitution,[status(thm)],[c61]) ).

cnf(c75,plain,
    multiply(inverse(multiply(inverse(X2),multiply(X3,X2))),inverse(inverse(X3))) = multiply(multiply(inverse(multiply(X3,X2)),inverse(inverse(X2))),inverse(inverse(X3))),
    inference(congruence,[status(thm)],[c74]) ).

cnf(c76,plain,
    multiply(multiply(inverse(multiply(X3,X2)),inverse(inverse(X2))),inverse(inverse(X3))) = multiply(inverse(multiply(X3,X2)),multiply(inverse(inverse(X2)),inverse(inverse(X3)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c77,plain,
    multiply(inverse(multiply(X3,X2)),multiply(inverse(inverse(X2)),inverse(inverse(X3)))) = multiply(multiply(inverse(X2),inverse(X3)),multiply(inverse(inverse(X2)),inverse(inverse(X3)))),
    inference(congruence,[status(thm)],[c61]) ).

cnf(c78,plain,
    multiply(multiply(inverse(X2),inverse(X3)),multiply(inverse(inverse(X2)),inverse(inverse(X3)))) = multiply(inverse(X2),multiply(inverse(X3),multiply(inverse(inverse(X2)),inverse(inverse(X3))))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c79,plain,
    multiply(inverse(inverse(X2)),inverse(inverse(X3))) = multiply(X2,inverse(inverse(X3))),
    inference(substitution,[status(thm)],[c13]) ).

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

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

cnf(c82,plain,
    multiply(inverse(inverse(X2)),identity) = inverse(inverse(X2)),
    inference(substitution,[status(thm)],[c20]) ).

cnf(c83,plain,
    inverse(inverse(X2)) = multiply(inverse(inverse(X2)),identity),
    inference(symmetry,[status(thm)],[c82]) ).

cnf(c84,plain,
    inverse(inverse(X2)) = X2,
    inference(transitivity,[status(thm)],[c83,c19]) ).

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

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

cnf(c87,plain,
    multiply(inverse(X2),multiply(inverse(X3),multiply(X2,inverse(inverse(X3))))) = multiply(inverse(X2),multiply(inverse(X3),multiply(X2,X3))),
    inference(congruence,[status(thm)],[c86]) ).

cnf(c88,plain,
    commutator(X2,X3) = multiply(inverse(X2),multiply(inverse(X3),multiply(X2,X3))),
    inference(substitution,[status(thm)],[c34]) ).

cnf(c89,plain,
    multiply(inverse(X2),multiply(inverse(X3),multiply(X2,X3))) = commutator(X2,X3),
    inference(symmetry,[status(thm)],[c88]) ).

cnf(c90,plain,
    multiply(inverse(X2),multiply(inverse(X3),multiply(X2,inverse(inverse(X3))))) = commutator(X2,X3),
    inference(transitivity,[status(thm)],[c87,c89]) ).

cnf(c91,plain,
    multiply(inverse(X2),multiply(inverse(X3),multiply(inverse(inverse(X2)),inverse(inverse(X3))))) = commutator(X2,X3),
    inference(transitivity,[status(thm)],[c81,c90]) ).

cnf(c92,plain,
    multiply(multiply(inverse(X2),inverse(X3)),multiply(inverse(inverse(X2)),inverse(inverse(X3)))) = commutator(X2,X3),
    inference(transitivity,[status(thm)],[c78,c91]) ).

cnf(c93,plain,
    multiply(inverse(multiply(X3,X2)),multiply(inverse(inverse(X2)),inverse(inverse(X3)))) = commutator(X2,X3),
    inference(transitivity,[status(thm)],[c77,c92]) ).

cnf(c94,plain,
    multiply(multiply(inverse(multiply(X3,X2)),inverse(inverse(X2))),inverse(inverse(X3))) = commutator(X2,X3),
    inference(transitivity,[status(thm)],[c76,c93]) ).

cnf(c95,plain,
    multiply(inverse(multiply(inverse(X2),multiply(X3,X2))),inverse(inverse(X3))) = commutator(X2,X3),
    inference(transitivity,[status(thm)],[c75,c94]) ).

cnf(c96,plain,
    inverse(multiply(inverse(X3),multiply(inverse(X2),multiply(X3,X2)))) = commutator(X2,X3),
    inference(transitivity,[status(thm)],[c73,c95]) ).

cnf(c97,plain,
    inverse(commutator(X3,X2)) = commutator(X2,X3),
    inference(transitivity,[status(thm)],[c72,c96]) ).

cnf(c98,plain,
    inverse(commutator(X2,multiply(X3,X2))) = commutator(multiply(X3,X2),X2),
    inference(substitution,[status(thm)],[c97]) ).

cnf(c99,plain,
    commutator(multiply(X3,X2),X2) = inverse(commutator(X2,multiply(X3,X2))),
    inference(symmetry,[status(thm)],[c98]) ).

cnf(c100,plain,
    multiply(inverse(X3),multiply(X3,commutator(X3,multiply(X2,X3)))) = commutator(X3,multiply(X2,X3)),
    inference(substitution,[status(thm)],[c9]) ).

cnf(c101,plain,
    commutator(X3,multiply(X2,X3)) = multiply(inverse(X3),multiply(X3,commutator(X3,multiply(X2,X3)))),
    inference(symmetry,[status(thm)],[c100]) ).

cnf(c102,plain,
    X2 = inverse(inverse(X2)),
    inference(symmetry,[status(thm)],[c84]) ).

cnf(c103,plain,
    commutator(X3,multiply(X2,commutator(X2,X3))) = commutator(inverse(inverse(X3)),multiply(X2,commutator(X2,X3))),
    inference(congruence,[status(thm)],[c102]) ).

cnf(c104,plain,
    multiply(X2,multiply(inverse(X2),multiply(inverse(X3),multiply(X2,X3)))) = multiply(inverse(X3),multiply(X2,X3)),
    inference(substitution,[status(thm)],[c26]) ).

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

cnf(c106,plain,
    commutator(X2,X3) = multiply(inverse(X2),multiply(inverse(X3),multiply(X2,X3))),
    inference(substitution,[status(thm)],[c34]) ).

cnf(c107,plain,
    multiply(inverse(X2),multiply(inverse(X3),multiply(X2,X3))) = commutator(X2,X3),
    inference(symmetry,[status(thm)],[c106]) ).

cnf(c108,plain,
    multiply(X2,multiply(inverse(X2),multiply(inverse(X3),multiply(X2,X3)))) = multiply(X2,commutator(X2,X3)),
    inference(congruence,[status(thm)],[c107]) ).

cnf(c109,plain,
    multiply(inverse(X3),multiply(X2,X3)) = multiply(X2,commutator(X2,X3)),
    inference(transitivity,[status(thm)],[c105,c108]) ).

cnf(c110,plain,
    multiply(X2,commutator(X2,X3)) = multiply(inverse(X3),multiply(X2,X3)),
    inference(symmetry,[status(thm)],[c109]) ).

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

cnf(c112,plain,
    commutator(inverse(inverse(X3)),multiply(inverse(X3),multiply(X2,X3))) = commutator(inverse(inverse(X3)),multiply(X2,X3)),
    inference(substitution,[status(thm)],[c69]) ).

cnf(c113,plain,
    commutator(inverse(inverse(X3)),multiply(X2,X3)) = commutator(X3,multiply(X2,X3)),
    inference(congruence,[status(thm)],[c84]) ).

cnf(c114,plain,
    commutator(inverse(inverse(X3)),multiply(inverse(X3),multiply(X2,X3))) = commutator(X3,multiply(X2,X3)),
    inference(transitivity,[status(thm)],[c112,c113]) ).

cnf(c115,plain,
    commutator(inverse(inverse(X3)),multiply(X2,commutator(X2,X3))) = commutator(X3,multiply(X2,X3)),
    inference(transitivity,[status(thm)],[c111,c114]) ).

cnf(c116,plain,
    commutator(X3,multiply(X2,commutator(X2,X3))) = commutator(X3,multiply(X2,X3)),
    inference(transitivity,[status(thm)],[c103,c115]) ).

cnf(c117,plain,
    commutator(X3,multiply(X2,X3)) = commutator(X3,multiply(X2,commutator(X2,X3))),
    inference(symmetry,[status(thm)],[c116]) ).

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

cnf(c119,plain,
    multiply(inverse(multiply(X2,commutator(X2,X3))),multiply(X3,multiply(X2,commutator(X2,X3)))) = multiply(X3,commutator(X3,multiply(X2,commutator(X2,X3)))),
    inference(substitution,[status(thm)],[c109]) ).

cnf(c120,plain,
    multiply(X3,commutator(X3,multiply(X2,commutator(X2,X3)))) = multiply(inverse(multiply(X2,commutator(X2,X3))),multiply(X3,multiply(X2,commutator(X2,X3)))),
    inference(symmetry,[status(thm)],[c119]) ).

cnf(c121,plain,
    inverse(multiply(X2,commutator(X2,X3))) = multiply(inverse(commutator(X2,X3)),inverse(X2)),
    inference(substitution,[status(thm)],[c61]) ).

cnf(c122,plain,
    multiply(inverse(multiply(X2,commutator(X2,X3))),multiply(X3,multiply(X2,commutator(X2,X3)))) = multiply(multiply(inverse(commutator(X2,X3)),inverse(X2)),multiply(X3,multiply(X2,commutator(X2,X3)))),
    inference(congruence,[status(thm)],[c121]) ).

cnf(c123,plain,
    multiply(multiply(inverse(commutator(X2,X3)),inverse(X2)),multiply(X3,multiply(X2,commutator(X2,X3)))) = multiply(inverse(commutator(X2,X3)),multiply(inverse(X2),multiply(X3,multiply(X2,commutator(X2,X3))))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c124,plain,
    inverse(commutator(X2,X3)) = commutator(X3,X2),
    inference(substitution,[status(thm)],[c97]) ).

cnf(c125,plain,
    multiply(inverse(commutator(X2,X3)),multiply(inverse(X2),multiply(X3,multiply(X2,commutator(X2,X3))))) = multiply(commutator(X3,X2),multiply(inverse(X2),multiply(X3,multiply(X2,commutator(X2,X3))))),
    inference(congruence,[status(thm)],[c124]) ).

cnf(c126,plain,
    multiply(inverse(inverse(X3)),multiply(X2,commutator(X2,X3))) = multiply(X3,multiply(X2,commutator(X2,X3))),
    inference(substitution,[status(thm)],[c13]) ).

cnf(c127,plain,
    multiply(X3,multiply(X2,commutator(X2,X3))) = multiply(inverse(inverse(X3)),multiply(X2,commutator(X2,X3))),
    inference(symmetry,[status(thm)],[c126]) ).

cnf(c128,plain,
    multiply(X2,commutator(X2,X3)) = multiply(inverse(X3),multiply(X2,X3)),
    inference(symmetry,[status(thm)],[c109]) ).

cnf(c129,plain,
    multiply(inverse(inverse(X3)),multiply(X2,commutator(X2,X3))) = multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X2,X3))),
    inference(congruence,[status(thm)],[c128]) ).

cnf(c130,plain,
    multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X2,X3))) = multiply(X2,X3),
    inference(substitution,[status(thm)],[c9]) ).

cnf(c131,plain,
    multiply(inverse(inverse(X3)),multiply(X2,commutator(X2,X3))) = multiply(X2,X3),
    inference(transitivity,[status(thm)],[c129,c130]) ).

cnf(c132,plain,
    multiply(X3,multiply(X2,commutator(X2,X3))) = multiply(X2,X3),
    inference(transitivity,[status(thm)],[c127,c131]) ).

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

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

cnf(c135,plain,
    multiply(inverse(X2),multiply(X2,X3)) = X3,
    inference(substitution,[status(thm)],[c9]) ).

cnf(c136,plain,
    multiply(commutator(X3,X2),multiply(inverse(X2),multiply(X2,X3))) = multiply(commutator(X3,X2),X3),
    inference(congruence,[status(thm)],[c135]) ).

cnf(c137,plain,
    X2 = multiply(X2,identity),
    inference(symmetry,[status(thm)],[c20]) ).

cnf(c138,plain,
    multiply(commutator(X3,X2),X3) = multiply(commutator(X3,X2),multiply(X3,identity)),
    inference(congruence,[status(thm)],[c137]) ).

cnf(c139,plain,
    commutator(commutator(X3,X3),X2) = commutator(X3,commutator(X3,X2)),
    inference(substitution,[status(thm)],[c29]) ).

cnf(c140,plain,
    commutator(X3,commutator(X3,X2)) = commutator(commutator(X3,X3),X2),
    inference(symmetry,[status(thm)],[c139]) ).

cnf(c141,plain,
    commutator(X2,X2) = multiply(inverse(X2),multiply(inverse(X2),multiply(X2,X2))),
    inference(substitution,[status(thm)],[c34]) ).

cnf(c142,plain,
    multiply(inverse(X2),multiply(X2,X2)) = X2,
    inference(substitution,[status(thm)],[c9]) ).

cnf(c143,plain,
    multiply(inverse(X2),multiply(inverse(X2),multiply(X2,X2))) = multiply(inverse(X2),X2),
    inference(congruence,[status(thm)],[c142]) ).

cnf(c144,plain,
    multiply(inverse(X2),multiply(inverse(X2),multiply(X2,X2))) = identity,
    inference(transitivity,[status(thm)],[c143,c5]) ).

cnf(c145,plain,
    commutator(X2,X2) = identity,
    inference(transitivity,[status(thm)],[c141,c144]) ).

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

cnf(c147,plain,
    commutator(identity,X2) = multiply(inverse(identity),multiply(inverse(X2),multiply(identity,X2))),
    inference(substitution,[status(thm)],[c34]) ).

cnf(c148,plain,
    multiply(inverse(X2),multiply(identity,X2)) = multiply(inverse(X2),X2),
    inference(congruence,[status(thm)],[c7]) ).

cnf(c149,plain,
    multiply(inverse(identity),multiply(inverse(X2),multiply(identity,X2))) = multiply(inverse(identity),multiply(inverse(X2),X2)),
    inference(congruence,[status(thm)],[c148]) ).

cnf(c150,plain,
    multiply(inverse(identity),multiply(inverse(X2),X2)) = multiply(inverse(identity),identity),
    inference(congruence,[status(thm)],[c5]) ).

cnf(c151,plain,
    multiply(inverse(identity),identity) = identity,
    inference(substitution,[status(thm)],[c5]) ).

cnf(c152,plain,
    multiply(inverse(identity),multiply(inverse(X2),X2)) = identity,
    inference(transitivity,[status(thm)],[c150,c151]) ).

cnf(c153,plain,
    multiply(inverse(identity),multiply(inverse(X2),multiply(identity,X2))) = identity,
    inference(transitivity,[status(thm)],[c149,c152]) ).

cnf(c154,plain,
    commutator(identity,X2) = identity,
    inference(transitivity,[status(thm)],[c147,c153]) ).

cnf(c155,plain,
    commutator(commutator(X3,X3),X2) = identity,
    inference(transitivity,[status(thm)],[c146,c154]) ).

cnf(c156,plain,
    commutator(X3,commutator(X3,X2)) = identity,
    inference(transitivity,[status(thm)],[c140,c155]) ).

cnf(c157,plain,
    identity = commutator(X3,commutator(X3,X2)),
    inference(symmetry,[status(thm)],[c156]) ).

cnf(c158,plain,
    multiply(X3,identity) = multiply(X3,commutator(X3,commutator(X3,X2))),
    inference(congruence,[status(thm)],[c157]) ).

cnf(c159,plain,
    multiply(commutator(X3,X2),multiply(X3,identity)) = multiply(commutator(X3,X2),multiply(X3,commutator(X3,commutator(X3,X2)))),
    inference(congruence,[status(thm)],[c158]) ).

cnf(c160,plain,
    multiply(commutator(X3,X2),multiply(X3,commutator(X3,commutator(X3,X2)))) = multiply(X3,commutator(X3,X2)),
    inference(substitution,[status(thm)],[c132]) ).

cnf(c161,plain,
    multiply(commutator(X3,X2),multiply(X3,identity)) = multiply(X3,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c159,c160]) ).

cnf(c162,plain,
    multiply(commutator(X3,X2),X3) = multiply(X3,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c138,c161]) ).

cnf(c163,plain,
    multiply(commutator(X3,X2),multiply(inverse(X2),multiply(X2,X3))) = multiply(X3,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c136,c162]) ).

cnf(c164,plain,
    multiply(commutator(X3,X2),multiply(inverse(X2),multiply(X3,multiply(X2,commutator(X2,X3))))) = multiply(X3,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c134,c163]) ).

cnf(c165,plain,
    multiply(inverse(commutator(X2,X3)),multiply(inverse(X2),multiply(X3,multiply(X2,commutator(X2,X3))))) = multiply(X3,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c125,c164]) ).

cnf(c166,plain,
    multiply(multiply(inverse(commutator(X2,X3)),inverse(X2)),multiply(X3,multiply(X2,commutator(X2,X3)))) = multiply(X3,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c123,c165]) ).

cnf(c167,plain,
    multiply(inverse(multiply(X2,commutator(X2,X3))),multiply(X3,multiply(X2,commutator(X2,X3)))) = multiply(X3,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c122,c166]) ).

cnf(c168,plain,
    multiply(X3,commutator(X3,multiply(X2,commutator(X2,X3)))) = multiply(X3,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c120,c167]) ).

cnf(c169,plain,
    multiply(X3,commutator(X3,multiply(X2,X3))) = multiply(X3,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c118,c168]) ).

cnf(c170,plain,
    multiply(inverse(X3),multiply(X3,commutator(X3,multiply(X2,X3)))) = multiply(inverse(X3),multiply(X3,commutator(X3,X2))),
    inference(congruence,[status(thm)],[c169]) ).

cnf(c171,plain,
    multiply(inverse(X3),multiply(X3,commutator(X3,X2))) = commutator(X3,X2),
    inference(substitution,[status(thm)],[c9]) ).

cnf(c172,plain,
    multiply(inverse(X3),multiply(X3,commutator(X3,multiply(X2,X3)))) = commutator(X3,X2),
    inference(transitivity,[status(thm)],[c170,c171]) ).

cnf(c173,plain,
    commutator(X3,multiply(X2,X3)) = commutator(X3,X2),
    inference(transitivity,[status(thm)],[c101,c172]) ).

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

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

cnf(c176,plain,
    inverse(commutator(X2,X3)) = commutator(X3,X2),
    inference(substitution,[status(thm)],[c97]) ).

cnf(c177,plain,
    inverse(commutator(X2,multiply(X3,X2))) = commutator(X3,X2),
    inference(transitivity,[status(thm)],[c175,c176]) ).

cnf(c178,plain,
    commutator(multiply(X3,X2),X2) = commutator(X3,X2),
    inference(transitivity,[status(thm)],[c99,c177]) ).

cnf(c179,plain,
    commutator(multiply(inverse(X3),multiply(X3,X2)),multiply(X3,X2)) = commutator(inverse(X3),multiply(X3,X2)),
    inference(substitution,[status(thm)],[c178]) ).

cnf(c180,plain,
    commutator(inverse(X3),multiply(X3,X2)) = commutator(multiply(inverse(X3),multiply(X3,X2)),multiply(X3,X2)),
    inference(symmetry,[status(thm)],[c179]) ).

cnf(c181,plain,
    commutator(multiply(inverse(X3),multiply(X3,X2)),multiply(X3,X2)) = commutator(X2,multiply(X3,X2)),
    inference(congruence,[status(thm)],[c9]) ).

cnf(c182,plain,
    commutator(X2,multiply(X3,X2)) = commutator(X2,X3),
    inference(substitution,[status(thm)],[c173]) ).

cnf(c183,plain,
    commutator(multiply(inverse(X3),multiply(X3,X2)),multiply(X3,X2)) = commutator(X2,X3),
    inference(transitivity,[status(thm)],[c181,c182]) ).

cnf(c184,plain,
    commutator(inverse(X3),multiply(X3,X2)) = commutator(X2,X3),
    inference(transitivity,[status(thm)],[c180,c183]) ).

cnf(c185,plain,
    commutator(inverse(X3),X2) = commutator(X2,X3),
    inference(transitivity,[status(thm)],[c70,c184]) ).

cnf(c186,plain,
    commutator(X2,multiply(inverse(X3),X2)) = commutator(X2,inverse(X3)),
    inference(substitution,[status(thm)],[c173]) ).

cnf(c187,plain,
    commutator(X2,inverse(X3)) = commutator(X2,multiply(inverse(X3),X2)),
    inference(symmetry,[status(thm)],[c186]) ).

cnf(c188,plain,
    X2 = multiply(X3,multiply(inverse(X3),X2)),
    inference(symmetry,[status(thm)],[c26]) ).

cnf(c189,plain,
    commutator(X2,multiply(inverse(X3),X2)) = commutator(multiply(X3,multiply(inverse(X3),X2)),multiply(inverse(X3),X2)),
    inference(congruence,[status(thm)],[c188]) ).

cnf(c190,plain,
    commutator(multiply(X3,multiply(inverse(X3),X2)),multiply(inverse(X3),X2)) = commutator(X3,multiply(inverse(X3),X2)),
    inference(substitution,[status(thm)],[c178]) ).

cnf(c191,plain,
    X2 = inverse(inverse(X2)),
    inference(symmetry,[status(thm)],[c84]) ).

cnf(c192,plain,
    commutator(X3,multiply(inverse(X3),X2)) = commutator(inverse(inverse(X3)),multiply(inverse(X3),X2)),
    inference(congruence,[status(thm)],[c191]) ).

cnf(c193,plain,
    commutator(inverse(inverse(X3)),multiply(inverse(X3),X2)) = commutator(inverse(inverse(X3)),X2),
    inference(substitution,[status(thm)],[c69]) ).

cnf(c194,plain,
    commutator(inverse(inverse(X3)),X2) = commutator(X3,X2),
    inference(congruence,[status(thm)],[c84]) ).

cnf(c195,plain,
    commutator(inverse(inverse(X3)),multiply(inverse(X3),X2)) = commutator(X3,X2),
    inference(transitivity,[status(thm)],[c193,c194]) ).

cnf(c196,plain,
    commutator(X3,multiply(inverse(X3),X2)) = commutator(X3,X2),
    inference(transitivity,[status(thm)],[c192,c195]) ).

cnf(c197,plain,
    commutator(multiply(X3,multiply(inverse(X3),X2)),multiply(inverse(X3),X2)) = commutator(X3,X2),
    inference(transitivity,[status(thm)],[c190,c196]) ).

cnf(c198,plain,
    commutator(X2,multiply(inverse(X3),X2)) = commutator(X3,X2),
    inference(transitivity,[status(thm)],[c189,c197]) ).

cnf(c199,plain,
    commutator(X2,inverse(X3)) = commutator(X3,X2),
    inference(transitivity,[status(thm)],[c187,c198]) ).

cnf(c200,plain,
    commutator(X3,inverse(X2)) = commutator(X2,X3),
    inference(substitution,[status(thm)],[c199]) ).

cnf(c201,plain,
    commutator(X2,X3) = commutator(X3,inverse(X2)),
    inference(symmetry,[status(thm)],[c200]) ).

cnf(c202,plain,
    commutator(inverse(X3),X2) = commutator(X3,inverse(X2)),
    inference(transitivity,[status(thm)],[c185,c201]) ).

cnf(c203,plain,
    commutator(inverse(commutator(X4,X3)),X2) = commutator(commutator(X4,X3),inverse(X2)),
    inference(substitution,[status(thm)],[c202]) ).

cnf(c204,plain,
    commutator(commutator(X4,X3),inverse(X2)) = commutator(inverse(commutator(X4,X3)),X2),
    inference(symmetry,[status(thm)],[c203]) ).

cnf(c205,plain,
    commutator(inverse(commutator(X4,X3)),X2) = commutator(X2,commutator(X4,X3)),
    inference(substitution,[status(thm)],[c185]) ).

cnf(c206,plain,
    inverse(commutator(commutator(X3,X2),X4)) = commutator(X4,commutator(X3,X2)),
    inference(substitution,[status(thm)],[c97]) ).

cnf(c207,plain,
    commutator(X4,commutator(X3,X2)) = inverse(commutator(commutator(X3,X2),X4)),
    inference(symmetry,[status(thm)],[c206]) ).

cnf(c208,plain,
    commutator(commutator(X3,X2),X4) = commutator(X3,commutator(X2,X4)),
    inference(substitution,[status(thm)],[c29]) ).

cnf(c209,plain,
    inverse(commutator(commutator(X3,X2),X4)) = inverse(commutator(X3,commutator(X2,X4))),
    inference(congruence,[status(thm)],[c208]) ).

cnf(c210,plain,
    inverse(commutator(X3,commutator(X2,X4))) = commutator(commutator(X2,X4),X3),
    inference(substitution,[status(thm)],[c97]) ).

cnf(c211,plain,
    commutator(commutator(X2,X4),X3) = commutator(X2,commutator(X4,X3)),
    inference(substitution,[status(thm)],[c29]) ).

cnf(c212,plain,
    inverse(commutator(X3,commutator(X2,X4))) = commutator(X2,commutator(X4,X3)),
    inference(transitivity,[status(thm)],[c210,c211]) ).

cnf(c213,plain,
    inverse(commutator(commutator(X3,X2),X4)) = commutator(X2,commutator(X4,X3)),
    inference(transitivity,[status(thm)],[c209,c212]) ).

cnf(c214,plain,
    commutator(X4,commutator(X3,X2)) = commutator(X2,commutator(X4,X3)),
    inference(transitivity,[status(thm)],[c207,c213]) ).

cnf(c215,plain,
    commutator(X2,commutator(X4,X3)) = commutator(X4,commutator(X3,X2)),
    inference(symmetry,[status(thm)],[c214]) ).

cnf(c216,plain,
    commutator(inverse(commutator(X4,X3)),X2) = commutator(X4,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c205,c215]) ).

cnf(c217,plain,
    commutator(commutator(X4,X3),inverse(X2)) = commutator(X4,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c204,c216]) ).

cnf(c218,plain,
    commutator(X4,commutator(X3,inverse(X2))) = commutator(X4,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c31,c217]) ).

cnf(c219,plain,
    commutator(X4,commutator(X3,X2)) = commutator(X4,commutator(X3,inverse(X2))),
    inference(symmetry,[status(thm)],[c218]) ).

cnf(c220,plain,
    multiply(commutator(X4,commutator(X3,X2)),inverse(X2)) = multiply(commutator(X4,commutator(X3,inverse(X2))),inverse(X2)),
    inference(congruence,[status(thm)],[c219]) ).

cnf(c221,plain,
    commutator(inverse(commutator(X3,X2)),X4) = commutator(X4,commutator(X3,X2)),
    inference(substitution,[status(thm)],[c185]) ).

cnf(c222,plain,
    commutator(X4,commutator(X3,X2)) = commutator(inverse(commutator(X3,X2)),X4),
    inference(symmetry,[status(thm)],[c221]) ).

cnf(c223,plain,
    commutator(inverse(commutator(X3,X2)),X4) = commutator(commutator(X2,X3),X4),
    inference(congruence,[status(thm)],[c97]) ).

cnf(c224,plain,
    commutator(commutator(X2,X3),X4) = commutator(X2,commutator(X3,X4)),
    inference(substitution,[status(thm)],[c29]) ).

cnf(c225,plain,
    commutator(X3,commutator(X4,X2)) = commutator(X2,commutator(X3,X4)),
    inference(substitution,[status(thm)],[c214]) ).

cnf(c226,plain,
    commutator(X2,commutator(X3,X4)) = commutator(X3,commutator(X4,X2)),
    inference(symmetry,[status(thm)],[c225]) ).

cnf(c227,plain,
    commutator(commutator(X2,X3),X4) = commutator(X3,commutator(X4,X2)),
    inference(transitivity,[status(thm)],[c224,c226]) ).

cnf(c228,plain,
    commutator(inverse(commutator(X3,X2)),X4) = commutator(X3,commutator(X4,X2)),
    inference(transitivity,[status(thm)],[c223,c227]) ).

cnf(c229,plain,
    commutator(X4,commutator(X3,X2)) = commutator(X3,commutator(X4,X2)),
    inference(transitivity,[status(thm)],[c222,c228]) ).

cnf(c230,plain,
    commutator(X3,commutator(X4,X2)) = commutator(X4,commutator(X3,X2)),
    inference(substitution,[status(thm)],[c229]) ).

cnf(c231,plain,
    commutator(X4,commutator(X3,X2)) = commutator(X3,commutator(X4,X2)),
    inference(symmetry,[status(thm)],[c230]) ).

cnf(c232,plain,
    multiply(commutator(X4,commutator(X3,X2)),X2) = multiply(commutator(X3,commutator(X4,X2)),X2),
    inference(congruence,[status(thm)],[c231]) ).

cnf(c233,plain,
    commutator(commutator(X3,X4),X2) = commutator(X3,commutator(X4,X2)),
    inference(substitution,[status(thm)],[c29]) ).

cnf(c234,plain,
    commutator(X3,commutator(X4,X2)) = commutator(commutator(X3,X4),X2),
    inference(symmetry,[status(thm)],[c233]) ).

cnf(c235,plain,
    multiply(commutator(X3,commutator(X4,X2)),X2) = multiply(commutator(commutator(X3,X4),X2),X2),
    inference(congruence,[status(thm)],[c234]) ).

cnf(c236,plain,
    X2 = multiply(X2,identity),
    inference(symmetry,[status(thm)],[c20]) ).

cnf(c237,plain,
    multiply(commutator(X3,X2),X2) = multiply(commutator(X3,X2),multiply(X2,identity)),
    inference(congruence,[status(thm)],[c236]) ).

cnf(c238,plain,
    commutator(commutator(X3,X2),X3) = commutator(X3,commutator(X2,X3)),
    inference(substitution,[status(thm)],[c29]) ).

cnf(c239,plain,
    commutator(X3,commutator(X2,X3)) = commutator(commutator(X3,X2),X3),
    inference(symmetry,[status(thm)],[c238]) ).

cnf(c240,plain,
    commutator(commutator(X3,X2),X3) = multiply(inverse(commutator(X3,X2)),multiply(inverse(X3),multiply(commutator(X3,X2),X3))),
    inference(substitution,[status(thm)],[c34]) ).

cnf(c241,plain,
    multiply(inverse(X3),multiply(commutator(X3,X2),X3)) = multiply(inverse(X3),multiply(X3,commutator(X3,X2))),
    inference(congruence,[status(thm)],[c162]) ).

cnf(c242,plain,
    multiply(inverse(commutator(X3,X2)),multiply(inverse(X3),multiply(commutator(X3,X2),X3))) = multiply(inverse(commutator(X3,X2)),multiply(inverse(X3),multiply(X3,commutator(X3,X2)))),
    inference(congruence,[status(thm)],[c241]) ).

cnf(c243,plain,
    multiply(inverse(X3),multiply(X3,commutator(X3,X2))) = commutator(X3,X2),
    inference(substitution,[status(thm)],[c9]) ).

cnf(c244,plain,
    multiply(inverse(commutator(X3,X2)),multiply(inverse(X3),multiply(X3,commutator(X3,X2)))) = multiply(inverse(commutator(X3,X2)),commutator(X3,X2)),
    inference(congruence,[status(thm)],[c243]) ).

cnf(c245,plain,
    multiply(inverse(commutator(X3,X2)),commutator(X3,X2)) = identity,
    inference(substitution,[status(thm)],[c5]) ).

cnf(c246,plain,
    multiply(inverse(commutator(X3,X2)),multiply(inverse(X3),multiply(X3,commutator(X3,X2)))) = identity,
    inference(transitivity,[status(thm)],[c244,c245]) ).

cnf(c247,plain,
    multiply(inverse(commutator(X3,X2)),multiply(inverse(X3),multiply(commutator(X3,X2),X3))) = identity,
    inference(transitivity,[status(thm)],[c242,c246]) ).

cnf(c248,plain,
    commutator(commutator(X3,X2),X3) = identity,
    inference(transitivity,[status(thm)],[c240,c247]) ).

cnf(c249,plain,
    commutator(X3,commutator(X2,X3)) = identity,
    inference(transitivity,[status(thm)],[c239,c248]) ).

cnf(c250,plain,
    commutator(X2,commutator(X3,X2)) = identity,
    inference(substitution,[status(thm)],[c249]) ).

cnf(c251,plain,
    identity = commutator(X2,commutator(X3,X2)),
    inference(symmetry,[status(thm)],[c250]) ).

cnf(c252,plain,
    multiply(X2,identity) = multiply(X2,commutator(X2,commutator(X3,X2))),
    inference(congruence,[status(thm)],[c251]) ).

cnf(c253,plain,
    multiply(commutator(X3,X2),multiply(X2,identity)) = multiply(commutator(X3,X2),multiply(X2,commutator(X2,commutator(X3,X2)))),
    inference(congruence,[status(thm)],[c252]) ).

cnf(c254,plain,
    multiply(commutator(X3,X2),multiply(X2,commutator(X2,commutator(X3,X2)))) = multiply(X2,commutator(X3,X2)),
    inference(substitution,[status(thm)],[c132]) ).

cnf(c255,plain,
    multiply(commutator(X3,X2),multiply(X2,identity)) = multiply(X2,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c253,c254]) ).

cnf(c256,plain,
    multiply(commutator(X3,X2),X2) = multiply(X2,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c237,c255]) ).

cnf(c257,plain,
    multiply(commutator(commutator(X3,X4),X2),X2) = multiply(X2,commutator(commutator(X3,X4),X2)),
    inference(substitution,[status(thm)],[c256]) ).

cnf(c258,plain,
    commutator(commutator(X3,X4),X2) = commutator(X3,commutator(X4,X2)),
    inference(substitution,[status(thm)],[c29]) ).

cnf(c259,plain,
    multiply(X2,commutator(commutator(X3,X4),X2)) = multiply(X2,commutator(X3,commutator(X4,X2))),
    inference(congruence,[status(thm)],[c258]) ).

cnf(c260,plain,
    commutator(X3,commutator(X4,X2)) = commutator(X4,commutator(X3,X2)),
    inference(substitution,[status(thm)],[c229]) ).

cnf(c261,plain,
    multiply(X2,commutator(X3,commutator(X4,X2))) = multiply(X2,commutator(X4,commutator(X3,X2))),
    inference(congruence,[status(thm)],[c260]) ).

cnf(c262,plain,
    multiply(X2,commutator(commutator(X3,X4),X2)) = multiply(X2,commutator(X4,commutator(X3,X2))),
    inference(transitivity,[status(thm)],[c259,c261]) ).

cnf(c263,plain,
    multiply(commutator(commutator(X3,X4),X2),X2) = multiply(X2,commutator(X4,commutator(X3,X2))),
    inference(transitivity,[status(thm)],[c257,c262]) ).

cnf(c264,plain,
    multiply(commutator(X3,commutator(X4,X2)),X2) = multiply(X2,commutator(X4,commutator(X3,X2))),
    inference(transitivity,[status(thm)],[c235,c263]) ).

cnf(c265,plain,
    multiply(commutator(X4,commutator(X3,X2)),X2) = multiply(X2,commutator(X4,commutator(X3,X2))),
    inference(transitivity,[status(thm)],[c232,c264]) ).

cnf(c266,plain,
    multiply(commutator(X4,commutator(X3,inverse(X2))),inverse(X2)) = multiply(inverse(X2),commutator(X4,commutator(X3,inverse(X2)))),
    inference(substitution,[status(thm)],[c265]) ).

cnf(c267,plain,
    multiply(inverse(X2),commutator(X4,commutator(X3,inverse(X2)))) = multiply(inverse(X2),commutator(X4,commutator(X3,X2))),
    inference(congruence,[status(thm)],[c218]) ).

cnf(c268,plain,
    commutator(X3,commutator(X2,X4)) = commutator(X4,commutator(X3,X2)),
    inference(substitution,[status(thm)],[c214]) ).

cnf(c269,plain,
    commutator(X4,commutator(X3,X2)) = commutator(X3,commutator(X2,X4)),
    inference(symmetry,[status(thm)],[c268]) ).

cnf(c270,plain,
    multiply(inverse(X2),commutator(X4,commutator(X3,X2))) = multiply(inverse(X2),commutator(X3,commutator(X2,X4))),
    inference(congruence,[status(thm)],[c269]) ).

cnf(c271,plain,
    commutator(X3,inverse(X2)) = commutator(X2,X3),
    inference(substitution,[status(thm)],[c199]) ).

cnf(c272,plain,
    commutator(X2,X3) = commutator(X3,inverse(X2)),
    inference(symmetry,[status(thm)],[c271]) ).

cnf(c273,plain,
    commutator(X3,commutator(X2,X4)) = commutator(X3,commutator(X4,inverse(X2))),
    inference(congruence,[status(thm)],[c272]) ).

cnf(c274,plain,
    multiply(inverse(X2),commutator(X3,commutator(X2,X4))) = multiply(inverse(X2),commutator(X3,commutator(X4,inverse(X2)))),
    inference(congruence,[status(thm)],[c273]) ).

cnf(c275,plain,
    commutator(X3,commutator(X4,inverse(X2))) = commutator(X3,commutator(X4,X2)),
    inference(substitution,[status(thm)],[c218]) ).

cnf(c276,plain,
    multiply(inverse(X2),commutator(X3,commutator(X4,inverse(X2)))) = multiply(inverse(X2),commutator(X3,commutator(X4,X2))),
    inference(congruence,[status(thm)],[c275]) ).

cnf(c277,plain,
    multiply(inverse(X2),commutator(X3,commutator(X2,X4))) = multiply(inverse(X2),commutator(X3,commutator(X4,X2))),
    inference(transitivity,[status(thm)],[c274,c276]) ).

cnf(c278,plain,
    multiply(inverse(X2),commutator(X4,commutator(X3,X2))) = multiply(inverse(X2),commutator(X3,commutator(X4,X2))),
    inference(transitivity,[status(thm)],[c270,c277]) ).

cnf(c279,plain,
    multiply(inverse(X2),commutator(X4,commutator(X3,inverse(X2)))) = multiply(inverse(X2),commutator(X3,commutator(X4,X2))),
    inference(transitivity,[status(thm)],[c267,c278]) ).

cnf(c280,plain,
    multiply(commutator(X4,commutator(X3,inverse(X2))),inverse(X2)) = multiply(inverse(X2),commutator(X3,commutator(X4,X2))),
    inference(transitivity,[status(thm)],[c266,c279]) ).

cnf(c281,plain,
    multiply(commutator(X4,commutator(X3,X2)),inverse(X2)) = multiply(inverse(X2),commutator(X3,commutator(X4,X2))),
    inference(transitivity,[status(thm)],[c220,c280]) ).

cnf(c282,plain,
    multiply(commutator(X3,commutator(X4,X2)),inverse(X2)) = multiply(inverse(X2),commutator(X4,commutator(X3,X2))),
    inference(substitution,[status(thm)],[c281]) ).

cnf(c283,plain,
    multiply(inverse(X2),commutator(X4,commutator(X3,X2))) = multiply(commutator(X3,commutator(X4,X2)),inverse(X2)),
    inference(symmetry,[status(thm)],[c282]) ).

cnf(c284,plain,
    multiply(X2,multiply(inverse(X2),commutator(X4,commutator(X3,X2)))) = multiply(X2,multiply(commutator(X3,commutator(X4,X2)),inverse(X2))),
    inference(congruence,[status(thm)],[c283]) ).

cnf(c285,plain,
    X2 = inverse(inverse(X2)),
    inference(symmetry,[status(thm)],[c84]) ).

cnf(c286,plain,
    multiply(X3,X2) = multiply(X3,inverse(inverse(X2))),
    inference(congruence,[status(thm)],[c285]) ).

cnf(c287,plain,
    commutator(X3,multiply(X4,X2)) = commutator(X3,multiply(X4,inverse(inverse(X2)))),
    inference(congruence,[status(thm)],[c286]) ).

cnf(c288,plain,
    multiply(commutator(X4,X3),commutator(X3,multiply(X4,X2))) = multiply(commutator(X4,X3),commutator(X3,multiply(X4,inverse(inverse(X2))))),
    inference(congruence,[status(thm)],[c287]) ).

cnf(c289,plain,
    multiply(inverse(inverse(X3)),inverse(X2)) = multiply(X3,inverse(X2)),
    inference(substitution,[status(thm)],[c13]) ).

cnf(c290,plain,
    multiply(X3,inverse(X2)) = multiply(inverse(inverse(X3)),inverse(X2)),
    inference(symmetry,[status(thm)],[c289]) ).

cnf(c291,plain,
    commutator(X3,multiply(X4,inverse(X2))) = commutator(X3,multiply(inverse(inverse(X4)),inverse(X2))),
    inference(congruence,[status(thm)],[c290]) ).

cnf(c292,plain,
    multiply(commutator(X4,X3),commutator(X3,multiply(X4,inverse(X2)))) = multiply(commutator(X4,X3),commutator(X3,multiply(inverse(inverse(X4)),inverse(X2)))),
    inference(congruence,[status(thm)],[c291]) ).

cnf(c293,plain,
    inverse(multiply(X2,inverse(X3))) = multiply(inverse(inverse(X3)),inverse(X2)),
    inference(substitution,[status(thm)],[c61]) ).

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

cnf(c295,plain,
    commutator(X3,multiply(inverse(inverse(X4)),inverse(X2))) = commutator(X3,inverse(multiply(X2,inverse(X4)))),
    inference(congruence,[status(thm)],[c294]) ).

cnf(c296,plain,
    multiply(commutator(X4,X3),commutator(X3,multiply(inverse(inverse(X4)),inverse(X2)))) = multiply(commutator(X4,X3),commutator(X3,inverse(multiply(X2,inverse(X4))))),
    inference(congruence,[status(thm)],[c295]) ).

cnf(c297,plain,
    commutator(inverse(X3),multiply(X2,inverse(X4))) = commutator(X3,inverse(multiply(X2,inverse(X4)))),
    inference(substitution,[status(thm)],[c202]) ).

cnf(c298,plain,
    commutator(X3,inverse(multiply(X2,inverse(X4)))) = commutator(inverse(X3),multiply(X2,inverse(X4))),
    inference(symmetry,[status(thm)],[c297]) ).

cnf(c299,plain,
    multiply(commutator(X4,X3),commutator(X3,inverse(multiply(X2,inverse(X4))))) = multiply(commutator(X4,X3),commutator(inverse(X3),multiply(X2,inverse(X4)))),
    inference(congruence,[status(thm)],[c298]) ).

cnf(c300,plain,
    multiply(multiply(inverse(X4),inverse(X3)),X2) = multiply(inverse(X4),multiply(inverse(X3),X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c301,plain,
    multiply(inverse(X4),multiply(inverse(X3),X2)) = multiply(multiply(inverse(X4),inverse(X3)),X2),
    inference(symmetry,[status(thm)],[c300]) ).

cnf(c302,plain,
    multiply(X3,multiply(inverse(X4),multiply(inverse(X3),X2))) = multiply(X3,multiply(multiply(inverse(X4),inverse(X3)),X2)),
    inference(congruence,[status(thm)],[c301]) ).

cnf(c303,plain,
    multiply(X4,multiply(X3,multiply(inverse(X4),multiply(inverse(X3),X2)))) = multiply(X4,multiply(X3,multiply(multiply(inverse(X4),inverse(X3)),X2))),
    inference(congruence,[status(thm)],[c302]) ).

cnf(c304,plain,
    multiply(multiply(X3,multiply(inverse(X4),inverse(X3))),X2) = multiply(X3,multiply(multiply(inverse(X4),inverse(X3)),X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c305,plain,
    multiply(X3,multiply(multiply(inverse(X4),inverse(X3)),X2)) = multiply(multiply(X3,multiply(inverse(X4),inverse(X3))),X2),
    inference(symmetry,[status(thm)],[c304]) ).

cnf(c306,plain,
    multiply(X4,multiply(X3,multiply(multiply(inverse(X4),inverse(X3)),X2))) = multiply(X4,multiply(multiply(X3,multiply(inverse(X4),inverse(X3))),X2)),
    inference(congruence,[status(thm)],[c305]) ).

cnf(c307,plain,
    multiply(multiply(X4,multiply(X3,multiply(inverse(X4),inverse(X3)))),X2) = multiply(X4,multiply(multiply(X3,multiply(inverse(X4),inverse(X3))),X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c308,plain,
    multiply(X4,multiply(multiply(X3,multiply(inverse(X4),inverse(X3))),X2)) = multiply(multiply(X4,multiply(X3,multiply(inverse(X4),inverse(X3)))),X2),
    inference(symmetry,[status(thm)],[c307]) ).

cnf(c309,plain,
    multiply(inverse(inverse(X3)),multiply(X2,multiply(inverse(X3),inverse(X2)))) = multiply(X3,multiply(X2,multiply(inverse(X3),inverse(X2)))),
    inference(substitution,[status(thm)],[c13]) ).

cnf(c310,plain,
    multiply(X3,multiply(X2,multiply(inverse(X3),inverse(X2)))) = multiply(inverse(inverse(X3)),multiply(X2,multiply(inverse(X3),inverse(X2)))),
    inference(symmetry,[status(thm)],[c309]) ).

cnf(c311,plain,
    multiply(inverse(inverse(X2)),multiply(X3,inverse(X2))) = multiply(X2,multiply(X3,inverse(X2))),
    inference(substitution,[status(thm)],[c13]) ).

cnf(c312,plain,
    multiply(X2,multiply(X3,inverse(X2))) = multiply(inverse(inverse(X2)),multiply(X3,inverse(X2))),
    inference(symmetry,[status(thm)],[c311]) ).

cnf(c313,plain,
    multiply(inverse(X3),multiply(X2,multiply(X3,inverse(X2)))) = multiply(inverse(X3),multiply(inverse(inverse(X2)),multiply(X3,inverse(X2)))),
    inference(congruence,[status(thm)],[c312]) ).

cnf(c314,plain,
    commutator(X3,inverse(X2)) = multiply(inverse(X3),multiply(inverse(inverse(X2)),multiply(X3,inverse(X2)))),
    inference(substitution,[status(thm)],[c34]) ).

cnf(c315,plain,
    multiply(inverse(X3),multiply(inverse(inverse(X2)),multiply(X3,inverse(X2)))) = commutator(X3,inverse(X2)),
    inference(symmetry,[status(thm)],[c314]) ).

cnf(c316,plain,
    multiply(inverse(X3),multiply(X2,multiply(X3,inverse(X2)))) = commutator(X3,inverse(X2)),
    inference(transitivity,[status(thm)],[c313,c315]) ).

cnf(c317,plain,
    multiply(inverse(inverse(X3)),multiply(X2,multiply(inverse(X3),inverse(X2)))) = commutator(inverse(X3),inverse(X2)),
    inference(substitution,[status(thm)],[c316]) ).

cnf(c318,plain,
    commutator(inverse(X3),inverse(X2)) = commutator(X3,inverse(inverse(X2))),
    inference(substitution,[status(thm)],[c202]) ).

cnf(c319,plain,
    commutator(X3,inverse(inverse(X2))) = commutator(X3,X2),
    inference(congruence,[status(thm)],[c84]) ).

cnf(c320,plain,
    commutator(inverse(X3),inverse(X2)) = commutator(X3,X2),
    inference(transitivity,[status(thm)],[c318,c319]) ).

cnf(c321,plain,
    multiply(inverse(inverse(X3)),multiply(X2,multiply(inverse(X3),inverse(X2)))) = commutator(X3,X2),
    inference(transitivity,[status(thm)],[c317,c320]) ).

cnf(c322,plain,
    multiply(X3,multiply(X2,multiply(inverse(X3),inverse(X2)))) = commutator(X3,X2),
    inference(transitivity,[status(thm)],[c310,c321]) ).

cnf(c323,plain,
    multiply(multiply(X4,multiply(X3,multiply(inverse(X4),inverse(X3)))),X2) = multiply(commutator(X4,X3),X2),
    inference(congruence,[status(thm)],[c322]) ).

cnf(c324,plain,
    multiply(X4,multiply(multiply(X3,multiply(inverse(X4),inverse(X3))),X2)) = multiply(commutator(X4,X3),X2),
    inference(transitivity,[status(thm)],[c308,c323]) ).

cnf(c325,plain,
    multiply(X4,multiply(X3,multiply(multiply(inverse(X4),inverse(X3)),X2))) = multiply(commutator(X4,X3),X2),
    inference(transitivity,[status(thm)],[c306,c324]) ).

cnf(c326,plain,
    multiply(X4,multiply(X3,multiply(inverse(X4),multiply(inverse(X3),X2)))) = multiply(commutator(X4,X3),X2),
    inference(transitivity,[status(thm)],[c303,c325]) ).

cnf(c327,plain,
    multiply(X4,multiply(X3,multiply(inverse(X4),multiply(inverse(X3),commutator(inverse(X3),multiply(X2,inverse(X4))))))) = multiply(commutator(X4,X3),commutator(inverse(X3),multiply(X2,inverse(X4)))),
    inference(substitution,[status(thm)],[c326]) ).

cnf(c328,plain,
    multiply(commutator(X4,X3),commutator(inverse(X3),multiply(X2,inverse(X4)))) = multiply(X4,multiply(X3,multiply(inverse(X4),multiply(inverse(X3),commutator(inverse(X3),multiply(X2,inverse(X4))))))),
    inference(symmetry,[status(thm)],[c327]) ).

cnf(c329,plain,
    multiply(inverse(X2),multiply(X2,multiply(X4,multiply(X3,commutator(X3,multiply(X2,X4)))))) = multiply(X4,multiply(X3,commutator(X3,multiply(X2,X4)))),
    inference(substitution,[status(thm)],[c9]) ).

cnf(c330,plain,
    multiply(X4,multiply(X3,commutator(X3,multiply(X2,X4)))) = multiply(inverse(X2),multiply(X2,multiply(X4,multiply(X3,commutator(X3,multiply(X2,X4)))))),
    inference(symmetry,[status(thm)],[c329]) ).

cnf(c331,plain,
    multiply(multiply(X4,X3),multiply(X2,commutator(X2,multiply(X4,X3)))) = multiply(X4,multiply(X3,multiply(X2,commutator(X2,multiply(X4,X3))))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c332,plain,
    multiply(X4,multiply(X3,multiply(X2,commutator(X2,multiply(X4,X3))))) = multiply(multiply(X4,X3),multiply(X2,commutator(X2,multiply(X4,X3)))),
    inference(symmetry,[status(thm)],[c331]) ).

cnf(c333,plain,
    multiply(multiply(X4,X3),multiply(X2,commutator(X2,multiply(X4,X3)))) = multiply(X2,multiply(X4,X3)),
    inference(substitution,[status(thm)],[c132]) ).

cnf(c334,plain,
    multiply(X4,multiply(X3,multiply(X2,commutator(X2,multiply(X4,X3))))) = multiply(X2,multiply(X4,X3)),
    inference(transitivity,[status(thm)],[c332,c333]) ).

cnf(c335,plain,
    multiply(X2,multiply(X4,multiply(X3,commutator(X3,multiply(X2,X4))))) = multiply(X3,multiply(X2,X4)),
    inference(substitution,[status(thm)],[c334]) ).

cnf(c336,plain,
    multiply(inverse(X2),multiply(X2,multiply(X4,multiply(X3,commutator(X3,multiply(X2,X4)))))) = multiply(inverse(X2),multiply(X3,multiply(X2,X4))),
    inference(congruence,[status(thm)],[c335]) ).

cnf(c337,plain,
    multiply(multiply(X3,X4),X2) = multiply(X3,multiply(X4,X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c338,plain,
    multiply(X3,multiply(X4,X2)) = multiply(multiply(X3,X4),X2),
    inference(symmetry,[status(thm)],[c337]) ).

cnf(c339,plain,
    multiply(inverse(X4),multiply(X3,multiply(X4,X2))) = multiply(inverse(X4),multiply(multiply(X3,X4),X2)),
    inference(congruence,[status(thm)],[c338]) ).

cnf(c340,plain,
    multiply(multiply(inverse(X4),multiply(X3,X4)),X2) = multiply(inverse(X4),multiply(multiply(X3,X4),X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c341,plain,
    multiply(inverse(X4),multiply(multiply(X3,X4),X2)) = multiply(multiply(inverse(X4),multiply(X3,X4)),X2),
    inference(symmetry,[status(thm)],[c340]) ).

cnf(c342,plain,
    multiply(multiply(inverse(X4),multiply(X3,X4)),X2) = multiply(multiply(X3,commutator(X3,X4)),X2),
    inference(congruence,[status(thm)],[c109]) ).

cnf(c343,plain,
    multiply(multiply(X3,commutator(X3,X4)),X2) = multiply(X3,multiply(commutator(X3,X4),X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c344,plain,
    multiply(multiply(inverse(X4),multiply(X3,X4)),X2) = multiply(X3,multiply(commutator(X3,X4),X2)),
    inference(transitivity,[status(thm)],[c342,c343]) ).

cnf(c345,plain,
    multiply(inverse(X4),multiply(multiply(X3,X4),X2)) = multiply(X3,multiply(commutator(X3,X4),X2)),
    inference(transitivity,[status(thm)],[c341,c344]) ).

cnf(c346,plain,
    multiply(inverse(X4),multiply(X3,multiply(X4,X2))) = multiply(X3,multiply(commutator(X3,X4),X2)),
    inference(transitivity,[status(thm)],[c339,c345]) ).

cnf(c347,plain,
    multiply(inverse(X2),multiply(X3,multiply(X2,X4))) = multiply(X3,multiply(commutator(X3,X2),X4)),
    inference(substitution,[status(thm)],[c346]) ).

cnf(c348,plain,
    multiply(inverse(X2),multiply(X2,multiply(X4,multiply(X3,commutator(X3,multiply(X2,X4)))))) = multiply(X3,multiply(commutator(X3,X2),X4)),
    inference(transitivity,[status(thm)],[c336,c347]) ).

cnf(c349,plain,
    multiply(X4,multiply(X3,commutator(X3,multiply(X2,X4)))) = multiply(X3,multiply(commutator(X3,X2),X4)),
    inference(transitivity,[status(thm)],[c330,c348]) ).

cnf(c350,plain,
    multiply(inverse(X4),multiply(inverse(X3),commutator(inverse(X3),multiply(X2,inverse(X4))))) = multiply(inverse(X3),multiply(commutator(inverse(X3),X2),inverse(X4))),
    inference(substitution,[status(thm)],[c349]) ).

cnf(c351,plain,
    multiply(X3,multiply(inverse(X4),multiply(inverse(X3),commutator(inverse(X3),multiply(X2,inverse(X4)))))) = multiply(X3,multiply(inverse(X3),multiply(commutator(inverse(X3),X2),inverse(X4)))),
    inference(congruence,[status(thm)],[c350]) ).

cnf(c352,plain,
    multiply(X4,multiply(X3,multiply(inverse(X4),multiply(inverse(X3),commutator(inverse(X3),multiply(X2,inverse(X4))))))) = multiply(X4,multiply(X3,multiply(inverse(X3),multiply(commutator(inverse(X3),X2),inverse(X4))))),
    inference(congruence,[status(thm)],[c351]) ).

cnf(c353,plain,
    multiply(X3,multiply(inverse(X3),multiply(commutator(inverse(X3),X2),inverse(X4)))) = multiply(commutator(inverse(X3),X2),inverse(X4)),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c354,plain,
    multiply(X4,multiply(X3,multiply(inverse(X3),multiply(commutator(inverse(X3),X2),inverse(X4))))) = multiply(X4,multiply(commutator(inverse(X3),X2),inverse(X4))),
    inference(congruence,[status(thm)],[c353]) ).

cnf(c355,plain,
    multiply(commutator(inverse(X3),X2),inverse(X4)) = multiply(commutator(X3,inverse(X2)),inverse(X4)),
    inference(congruence,[status(thm)],[c202]) ).

cnf(c356,plain,
    multiply(X4,multiply(commutator(inverse(X3),X2),inverse(X4))) = multiply(X4,multiply(commutator(X3,inverse(X2)),inverse(X4))),
    inference(congruence,[status(thm)],[c355]) ).

cnf(c357,plain,
    multiply(X4,multiply(X3,multiply(inverse(X3),multiply(commutator(inverse(X3),X2),inverse(X4))))) = multiply(X4,multiply(commutator(X3,inverse(X2)),inverse(X4))),
    inference(transitivity,[status(thm)],[c354,c356]) ).

cnf(c358,plain,
    multiply(X4,multiply(X3,multiply(inverse(X4),multiply(inverse(X3),commutator(inverse(X3),multiply(X2,inverse(X4))))))) = multiply(X4,multiply(commutator(X3,inverse(X2)),inverse(X4))),
    inference(transitivity,[status(thm)],[c352,c357]) ).

cnf(c359,plain,
    multiply(commutator(X4,X3),commutator(inverse(X3),multiply(X2,inverse(X4)))) = multiply(X4,multiply(commutator(X3,inverse(X2)),inverse(X4))),
    inference(transitivity,[status(thm)],[c328,c358]) ).

cnf(c360,plain,
    multiply(commutator(X4,X3),commutator(X3,inverse(multiply(X2,inverse(X4))))) = multiply(X4,multiply(commutator(X3,inverse(X2)),inverse(X4))),
    inference(transitivity,[status(thm)],[c299,c359]) ).

cnf(c361,plain,
    multiply(commutator(X4,X3),commutator(X3,multiply(inverse(inverse(X4)),inverse(X2)))) = multiply(X4,multiply(commutator(X3,inverse(X2)),inverse(X4))),
    inference(transitivity,[status(thm)],[c296,c360]) ).

cnf(c362,plain,
    multiply(commutator(X4,X3),commutator(X3,multiply(X4,inverse(X2)))) = multiply(X4,multiply(commutator(X3,inverse(X2)),inverse(X4))),
    inference(transitivity,[status(thm)],[c292,c361]) ).

cnf(c363,plain,
    multiply(commutator(X4,X3),commutator(X3,multiply(X4,inverse(inverse(X2))))) = multiply(X4,multiply(commutator(X3,inverse(inverse(X2))),inverse(X4))),
    inference(substitution,[status(thm)],[c362]) ).

cnf(c364,plain,
    commutator(X3,inverse(inverse(X2))) = commutator(X3,X2),
    inference(congruence,[status(thm)],[c84]) ).

cnf(c365,plain,
    multiply(commutator(X3,inverse(inverse(X2))),inverse(X4)) = multiply(commutator(X3,X2),inverse(X4)),
    inference(congruence,[status(thm)],[c364]) ).

cnf(c366,plain,
    multiply(X4,multiply(commutator(X3,inverse(inverse(X2))),inverse(X4))) = multiply(X4,multiply(commutator(X3,X2),inverse(X4))),
    inference(congruence,[status(thm)],[c365]) ).

cnf(c367,plain,
    multiply(commutator(X4,X3),commutator(X3,multiply(X4,inverse(inverse(X2))))) = multiply(X4,multiply(commutator(X3,X2),inverse(X4))),
    inference(transitivity,[status(thm)],[c363,c366]) ).

cnf(c368,plain,
    multiply(commutator(X4,X3),commutator(X3,multiply(X4,X2))) = multiply(X4,multiply(commutator(X3,X2),inverse(X4))),
    inference(transitivity,[status(thm)],[c288,c367]) ).

cnf(c369,plain,
    multiply(commutator(X2,X3),commutator(X3,multiply(X2,commutator(X4,X2)))) = multiply(X2,multiply(commutator(X3,commutator(X4,X2)),inverse(X2))),
    inference(substitution,[status(thm)],[c368]) ).

cnf(c370,plain,
    multiply(X2,multiply(commutator(X3,commutator(X4,X2)),inverse(X2))) = multiply(commutator(X2,X3),commutator(X3,multiply(X2,commutator(X4,X2)))),
    inference(symmetry,[status(thm)],[c369]) ).

cnf(c371,plain,
    multiply(inverse(inverse(X2)),multiply(X3,inverse(X2))) = multiply(X2,multiply(X3,inverse(X2))),
    inference(substitution,[status(thm)],[c13]) ).

cnf(c372,plain,
    multiply(X2,multiply(X3,inverse(X2))) = multiply(inverse(inverse(X2)),multiply(X3,inverse(X2))),
    inference(symmetry,[status(thm)],[c371]) ).

cnf(c373,plain,
    multiply(inverse(inverse(X2)),multiply(X3,inverse(X2))) = multiply(X3,commutator(X3,inverse(X2))),
    inference(substitution,[status(thm)],[c109]) ).

cnf(c374,plain,
    multiply(X2,multiply(X3,inverse(X2))) = multiply(X3,commutator(X3,inverse(X2))),
    inference(transitivity,[status(thm)],[c372,c373]) ).

cnf(c375,plain,
    multiply(X3,multiply(X2,inverse(X3))) = multiply(X2,commutator(X2,inverse(X3))),
    inference(substitution,[status(thm)],[c374]) ).

cnf(c376,plain,
    commutator(inverse(inverse(X3)),X2) = commutator(X2,inverse(X3)),
    inference(substitution,[status(thm)],[c185]) ).

cnf(c377,plain,
    commutator(X2,inverse(X3)) = commutator(inverse(inverse(X3)),X2),
    inference(symmetry,[status(thm)],[c376]) ).

cnf(c378,plain,
    multiply(X2,commutator(X2,inverse(X3))) = multiply(X2,commutator(inverse(inverse(X3)),X2)),
    inference(congruence,[status(thm)],[c377]) ).

cnf(c379,plain,
    commutator(inverse(inverse(X3)),X2) = commutator(inverse(X3),inverse(X2)),
    inference(substitution,[status(thm)],[c202]) ).

cnf(c380,plain,
    multiply(X2,commutator(inverse(inverse(X3)),X2)) = multiply(X2,commutator(inverse(X3),inverse(X2))),
    inference(congruence,[status(thm)],[c379]) ).

cnf(c381,plain,
    commutator(inverse(X3),inverse(X2)) = commutator(X3,inverse(inverse(X2))),
    inference(substitution,[status(thm)],[c202]) ).

cnf(c382,plain,
    multiply(X2,commutator(inverse(X3),inverse(X2))) = multiply(X2,commutator(X3,inverse(inverse(X2)))),
    inference(congruence,[status(thm)],[c381]) ).

cnf(c383,plain,
    commutator(X3,inverse(inverse(X2))) = commutator(X3,X2),
    inference(congruence,[status(thm)],[c84]) ).

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

cnf(c385,plain,
    multiply(X2,commutator(inverse(X3),inverse(X2))) = multiply(X2,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c382,c384]) ).

cnf(c386,plain,
    multiply(X2,commutator(inverse(inverse(X3)),X2)) = multiply(X2,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c380,c385]) ).

cnf(c387,plain,
    multiply(X2,commutator(X2,inverse(X3))) = multiply(X2,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c378,c386]) ).

cnf(c388,plain,
    multiply(X3,multiply(X2,inverse(X3))) = multiply(X2,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c375,c387]) ).

cnf(c389,plain,
    multiply(X2,multiply(X3,inverse(X2))) = multiply(X3,commutator(X2,X3)),
    inference(substitution,[status(thm)],[c388]) ).

cnf(c390,plain,
    multiply(X3,commutator(X2,X3)) = multiply(X2,multiply(X3,inverse(X2))),
    inference(symmetry,[status(thm)],[c389]) ).

cnf(c391,plain,
    commutator(X4,multiply(X3,commutator(X2,X3))) = commutator(X4,multiply(X2,multiply(X3,inverse(X2)))),
    inference(congruence,[status(thm)],[c390]) ).

cnf(c392,plain,
    multiply(inverse(X4),multiply(X4,commutator(X4,multiply(X2,X3)))) = commutator(X4,multiply(X2,X3)),
    inference(substitution,[status(thm)],[c9]) ).

cnf(c393,plain,
    commutator(X4,multiply(X2,X3)) = multiply(inverse(X4),multiply(X4,commutator(X4,multiply(X2,X3)))),
    inference(symmetry,[status(thm)],[c392]) ).

cnf(c394,plain,
    multiply(inverse(X3),multiply(X3,commutator(X4,multiply(X2,X3)))) = commutator(X4,multiply(X2,X3)),
    inference(substitution,[status(thm)],[c9]) ).

cnf(c395,plain,
    commutator(X4,multiply(X2,X3)) = multiply(inverse(X3),multiply(X3,commutator(X4,multiply(X2,X3)))),
    inference(symmetry,[status(thm)],[c394]) ).

cnf(c396,plain,
    multiply(X4,commutator(X4,multiply(X2,X3))) = multiply(X4,multiply(inverse(X3),multiply(X3,commutator(X4,multiply(X2,X3))))),
    inference(congruence,[status(thm)],[c395]) ).

cnf(c397,plain,
    multiply(inverse(inverse(X4)),multiply(inverse(X3),multiply(X3,commutator(X4,multiply(X2,X3))))) = multiply(X4,multiply(inverse(X3),multiply(X3,commutator(X4,multiply(X2,X3))))),
    inference(substitution,[status(thm)],[c13]) ).

cnf(c398,plain,
    multiply(X4,multiply(inverse(X3),multiply(X3,commutator(X4,multiply(X2,X3))))) = multiply(inverse(inverse(X4)),multiply(inverse(X3),multiply(X3,commutator(X4,multiply(X2,X3))))),
    inference(symmetry,[status(thm)],[c397]) ).

cnf(c399,plain,
    multiply(multiply(inverse(inverse(X4)),inverse(X3)),multiply(X3,commutator(X4,multiply(X2,X3)))) = multiply(inverse(inverse(X4)),multiply(inverse(X3),multiply(X3,commutator(X4,multiply(X2,X3))))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c400,plain,
    multiply(inverse(inverse(X4)),multiply(inverse(X3),multiply(X3,commutator(X4,multiply(X2,X3))))) = multiply(multiply(inverse(inverse(X4)),inverse(X3)),multiply(X3,commutator(X4,multiply(X2,X3)))),
    inference(symmetry,[status(thm)],[c399]) ).

cnf(c401,plain,
    inverse(multiply(X2,inverse(X3))) = multiply(inverse(inverse(X3)),inverse(X2)),
    inference(substitution,[status(thm)],[c61]) ).

cnf(c402,plain,
    multiply(inverse(inverse(X3)),inverse(X2)) = inverse(multiply(X2,inverse(X3))),
    inference(symmetry,[status(thm)],[c401]) ).

cnf(c403,plain,
    multiply(multiply(inverse(inverse(X4)),inverse(X3)),multiply(X3,commutator(X4,multiply(X2,X3)))) = multiply(inverse(multiply(X3,inverse(X4))),multiply(X3,commutator(X4,multiply(X2,X3)))),
    inference(congruence,[status(thm)],[c402]) ).

cnf(c404,plain,
    multiply(inverse(X3),multiply(X4,multiply(X3,multiply(X2,inverse(X4))))) = multiply(X4,multiply(commutator(X4,X3),multiply(X2,inverse(X4)))),
    inference(substitution,[status(thm)],[c346]) ).

cnf(c405,plain,
    multiply(X4,multiply(commutator(X4,X3),multiply(X2,inverse(X4)))) = multiply(inverse(X3),multiply(X4,multiply(X3,multiply(X2,inverse(X4))))),
    inference(symmetry,[status(thm)],[c404]) ).

cnf(c406,plain,
    X2 = inverse(inverse(X2)),
    inference(symmetry,[status(thm)],[c84]) ).

cnf(c407,plain,
    multiply(X3,X2) = multiply(X3,inverse(inverse(X2))),
    inference(congruence,[status(thm)],[c406]) ).

cnf(c408,plain,
    commutator(X2,multiply(X4,X3)) = commutator(X2,multiply(X4,inverse(inverse(X3)))),
    inference(congruence,[status(thm)],[c407]) ).

cnf(c409,plain,
    multiply(X3,commutator(X2,multiply(X4,X3))) = multiply(X3,commutator(X2,multiply(X4,inverse(inverse(X3))))),
    inference(congruence,[status(thm)],[c408]) ).

cnf(c410,plain,
    multiply(X4,multiply(X3,commutator(X2,multiply(X4,X3)))) = multiply(X4,multiply(X3,commutator(X2,multiply(X4,inverse(inverse(X3)))))),
    inference(congruence,[status(thm)],[c409]) ).

cnf(c411,plain,
    multiply(inverse(inverse(X3)),inverse(inverse(X2))) = multiply(X3,inverse(inverse(X2))),
    inference(substitution,[status(thm)],[c13]) ).

cnf(c412,plain,
    multiply(X3,inverse(inverse(X2))) = multiply(inverse(inverse(X3)),inverse(inverse(X2))),
    inference(symmetry,[status(thm)],[c411]) ).

cnf(c413,plain,
    commutator(X2,multiply(X4,inverse(inverse(X3)))) = commutator(X2,multiply(inverse(inverse(X4)),inverse(inverse(X3)))),
    inference(congruence,[status(thm)],[c412]) ).

cnf(c414,plain,
    multiply(X3,commutator(X2,multiply(X4,inverse(inverse(X3))))) = multiply(X3,commutator(X2,multiply(inverse(inverse(X4)),inverse(inverse(X3))))),
    inference(congruence,[status(thm)],[c413]) ).

cnf(c415,plain,
    multiply(X4,multiply(X3,commutator(X2,multiply(X4,inverse(inverse(X3)))))) = multiply(X4,multiply(X3,commutator(X2,multiply(inverse(inverse(X4)),inverse(inverse(X3)))))),
    inference(congruence,[status(thm)],[c414]) ).

cnf(c416,plain,
    inverse(multiply(inverse(X2),inverse(X3))) = multiply(inverse(inverse(X3)),inverse(inverse(X2))),
    inference(substitution,[status(thm)],[c61]) ).

cnf(c417,plain,
    multiply(inverse(inverse(X3)),inverse(inverse(X2))) = inverse(multiply(inverse(X2),inverse(X3))),
    inference(symmetry,[status(thm)],[c416]) ).

cnf(c418,plain,
    commutator(X2,multiply(inverse(inverse(X4)),inverse(inverse(X3)))) = commutator(X2,inverse(multiply(inverse(X3),inverse(X4)))),
    inference(congruence,[status(thm)],[c417]) ).

cnf(c419,plain,
    multiply(X3,commutator(X2,multiply(inverse(inverse(X4)),inverse(inverse(X3))))) = multiply(X3,commutator(X2,inverse(multiply(inverse(X3),inverse(X4))))),
    inference(congruence,[status(thm)],[c418]) ).

cnf(c420,plain,
    multiply(X4,multiply(X3,commutator(X2,multiply(inverse(inverse(X4)),inverse(inverse(X3)))))) = multiply(X4,multiply(X3,commutator(X2,inverse(multiply(inverse(X3),inverse(X4)))))),
    inference(congruence,[status(thm)],[c419]) ).

cnf(c421,plain,
    commutator(inverse(X2),multiply(inverse(X3),inverse(X4))) = commutator(X2,inverse(multiply(inverse(X3),inverse(X4)))),
    inference(substitution,[status(thm)],[c202]) ).

cnf(c422,plain,
    commutator(X2,inverse(multiply(inverse(X3),inverse(X4)))) = commutator(inverse(X2),multiply(inverse(X3),inverse(X4))),
    inference(symmetry,[status(thm)],[c421]) ).

cnf(c423,plain,
    multiply(X3,commutator(X2,inverse(multiply(inverse(X3),inverse(X4))))) = multiply(X3,commutator(inverse(X2),multiply(inverse(X3),inverse(X4)))),
    inference(congruence,[status(thm)],[c422]) ).

cnf(c424,plain,
    multiply(X4,multiply(X3,commutator(X2,inverse(multiply(inverse(X3),inverse(X4)))))) = multiply(X4,multiply(X3,commutator(inverse(X2),multiply(inverse(X3),inverse(X4))))),
    inference(congruence,[status(thm)],[c423]) ).

cnf(c425,plain,
    multiply(inverse(X2),inverse(X3)) = inverse(multiply(X3,X2)),
    inference(symmetry,[status(thm)],[c61]) ).

cnf(c426,plain,
    commutator(X2,multiply(inverse(X3),inverse(X4))) = commutator(X2,inverse(multiply(X4,X3))),
    inference(congruence,[status(thm)],[c425]) ).

cnf(c427,plain,
    multiply(X3,commutator(X2,multiply(inverse(X3),inverse(X4)))) = multiply(X3,commutator(X2,inverse(multiply(X4,X3)))),
    inference(congruence,[status(thm)],[c426]) ).

cnf(c428,plain,
    multiply(X4,multiply(X3,commutator(X2,multiply(inverse(X3),inverse(X4))))) = multiply(X4,multiply(X3,commutator(X2,inverse(multiply(X4,X3))))),
    inference(congruence,[status(thm)],[c427]) ).

cnf(c429,plain,
    commutator(X2,inverse(multiply(X4,X3))) = commutator(multiply(X4,X3),X2),
    inference(substitution,[status(thm)],[c199]) ).

cnf(c430,plain,
    multiply(X3,commutator(X2,inverse(multiply(X4,X3)))) = multiply(X3,commutator(multiply(X4,X3),X2)),
    inference(congruence,[status(thm)],[c429]) ).

cnf(c431,plain,
    multiply(X4,multiply(X3,commutator(X2,inverse(multiply(X4,X3))))) = multiply(X4,multiply(X3,commutator(multiply(X4,X3),X2))),
    inference(congruence,[status(thm)],[c430]) ).

cnf(c432,plain,
    multiply(multiply(X4,X3),commutator(multiply(X4,X3),X2)) = multiply(X4,multiply(X3,commutator(multiply(X4,X3),X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c433,plain,
    multiply(X4,multiply(X3,commutator(multiply(X4,X3),X2))) = multiply(multiply(X4,X3),commutator(multiply(X4,X3),X2)),
    inference(symmetry,[status(thm)],[c432]) ).

cnf(c434,plain,
    multiply(inverse(X2),multiply(multiply(X4,X3),X2)) = multiply(multiply(X4,X3),commutator(multiply(X4,X3),X2)),
    inference(substitution,[status(thm)],[c109]) ).

cnf(c435,plain,
    multiply(multiply(X4,X3),commutator(multiply(X4,X3),X2)) = multiply(inverse(X2),multiply(multiply(X4,X3),X2)),
    inference(symmetry,[status(thm)],[c434]) ).

cnf(c436,plain,
    multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X3,X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c437,plain,
    multiply(inverse(X2),multiply(multiply(X4,X3),X2)) = multiply(inverse(X2),multiply(X4,multiply(X3,X2))),
    inference(congruence,[status(thm)],[c436]) ).

cnf(c438,plain,
    multiply(multiply(X4,X3),commutator(multiply(X4,X3),X2)) = multiply(inverse(X2),multiply(X4,multiply(X3,X2))),
    inference(transitivity,[status(thm)],[c435,c437]) ).

cnf(c439,plain,
    multiply(X4,multiply(X3,commutator(multiply(X4,X3),X2))) = multiply(inverse(X2),multiply(X4,multiply(X3,X2))),
    inference(transitivity,[status(thm)],[c433,c438]) ).

cnf(c440,plain,
    multiply(X4,multiply(X3,commutator(X2,inverse(multiply(X4,X3))))) = multiply(inverse(X2),multiply(X4,multiply(X3,X2))),
    inference(transitivity,[status(thm)],[c431,c439]) ).

cnf(c441,plain,
    multiply(X4,multiply(X3,commutator(X2,multiply(inverse(X3),inverse(X4))))) = multiply(inverse(X2),multiply(X4,multiply(X3,X2))),
    inference(transitivity,[status(thm)],[c428,c440]) ).

cnf(c442,plain,
    multiply(X4,multiply(X3,commutator(inverse(X2),multiply(inverse(X3),inverse(X4))))) = multiply(inverse(inverse(X2)),multiply(X4,multiply(X3,inverse(X2)))),
    inference(substitution,[status(thm)],[c441]) ).

cnf(c443,plain,
    multiply(inverse(inverse(X2)),multiply(X4,multiply(X3,inverse(X2)))) = multiply(X2,multiply(X4,multiply(X3,inverse(X2)))),
    inference(congruence,[status(thm)],[c84]) ).

cnf(c444,plain,
    multiply(X4,multiply(X3,commutator(inverse(X2),multiply(inverse(X3),inverse(X4))))) = multiply(X2,multiply(X4,multiply(X3,inverse(X2)))),
    inference(transitivity,[status(thm)],[c442,c443]) ).

cnf(c445,plain,
    multiply(X4,multiply(X3,commutator(X2,inverse(multiply(inverse(X3),inverse(X4)))))) = multiply(X2,multiply(X4,multiply(X3,inverse(X2)))),
    inference(transitivity,[status(thm)],[c424,c444]) ).

cnf(c446,plain,
    multiply(X4,multiply(X3,commutator(X2,multiply(inverse(inverse(X4)),inverse(inverse(X3)))))) = multiply(X2,multiply(X4,multiply(X3,inverse(X2)))),
    inference(transitivity,[status(thm)],[c420,c445]) ).

cnf(c447,plain,
    multiply(X4,multiply(X3,commutator(X2,multiply(X4,inverse(inverse(X3)))))) = multiply(X2,multiply(X4,multiply(X3,inverse(X2)))),
    inference(transitivity,[status(thm)],[c415,c446]) ).

cnf(c448,plain,
    multiply(X4,multiply(X3,commutator(X2,multiply(X4,X3)))) = multiply(X2,multiply(X4,multiply(X3,inverse(X2)))),
    inference(transitivity,[status(thm)],[c410,c447]) ).

cnf(c449,plain,
    multiply(X3,multiply(X2,commutator(X4,multiply(X3,X2)))) = multiply(X4,multiply(X3,multiply(X2,inverse(X4)))),
    inference(substitution,[status(thm)],[c448]) ).

cnf(c450,plain,
    multiply(X4,multiply(X3,multiply(X2,inverse(X4)))) = multiply(X3,multiply(X2,commutator(X4,multiply(X3,X2)))),
    inference(symmetry,[status(thm)],[c449]) ).

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

cnf(c452,plain,
    multiply(inverse(X3),multiply(X3,multiply(X2,commutator(X4,multiply(X3,X2))))) = multiply(X2,commutator(X4,multiply(X3,X2))),
    inference(substitution,[status(thm)],[c9]) ).

cnf(c453,plain,
    multiply(inverse(X3),multiply(X4,multiply(X3,multiply(X2,inverse(X4))))) = multiply(X2,commutator(X4,multiply(X3,X2))),
    inference(transitivity,[status(thm)],[c451,c452]) ).

cnf(c454,plain,
    multiply(X4,multiply(commutator(X4,X3),multiply(X2,inverse(X4)))) = multiply(X2,commutator(X4,multiply(X3,X2))),
    inference(transitivity,[status(thm)],[c405,c453]) ).

cnf(c455,plain,
    multiply(X4,multiply(commutator(X4,X2),multiply(X3,inverse(X4)))) = multiply(X3,commutator(X4,multiply(X2,X3))),
    inference(substitution,[status(thm)],[c454]) ).

cnf(c456,plain,
    multiply(X3,commutator(X4,multiply(X2,X3))) = multiply(X4,multiply(commutator(X4,X2),multiply(X3,inverse(X4)))),
    inference(symmetry,[status(thm)],[c455]) ).

cnf(c457,plain,
    multiply(inverse(multiply(X3,inverse(X4))),multiply(X3,commutator(X4,multiply(X2,X3)))) = multiply(inverse(multiply(X3,inverse(X4))),multiply(X4,multiply(commutator(X4,X2),multiply(X3,inverse(X4))))),
    inference(congruence,[status(thm)],[c456]) ).

cnf(c458,plain,
    multiply(inverse(inverse(X4)),multiply(X3,multiply(commutator(X3,X4),X2))) = multiply(X4,multiply(X3,multiply(commutator(X3,X4),X2))),
    inference(substitution,[status(thm)],[c13]) ).

cnf(c459,plain,
    multiply(X4,multiply(X3,multiply(commutator(X3,X4),X2))) = multiply(inverse(inverse(X4)),multiply(X3,multiply(commutator(X3,X4),X2))),
    inference(symmetry,[status(thm)],[c458]) ).

cnf(c460,plain,
    multiply(X3,multiply(commutator(X3,X4),X2)) = multiply(inverse(X4),multiply(X3,multiply(X4,X2))),
    inference(symmetry,[status(thm)],[c346]) ).

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

cnf(c462,plain,
    multiply(inverse(inverse(X4)),multiply(inverse(X4),multiply(X3,multiply(X4,X2)))) = multiply(X3,multiply(X4,X2)),
    inference(substitution,[status(thm)],[c9]) ).

cnf(c463,plain,
    multiply(inverse(inverse(X4)),multiply(X3,multiply(commutator(X3,X4),X2))) = multiply(X3,multiply(X4,X2)),
    inference(transitivity,[status(thm)],[c461,c462]) ).

cnf(c464,plain,
    multiply(X4,multiply(X3,multiply(commutator(X3,X4),X2))) = multiply(X3,multiply(X4,X2)),
    inference(transitivity,[status(thm)],[c459,c463]) ).

cnf(c465,plain,
    multiply(X3,multiply(X4,multiply(commutator(X4,X3),commutator(X3,multiply(X4,X2))))) = multiply(X4,multiply(X3,commutator(X3,multiply(X4,X2)))),
    inference(substitution,[status(thm)],[c464]) ).

cnf(c466,plain,
    multiply(X4,multiply(X3,commutator(X3,multiply(X4,X2)))) = multiply(X3,multiply(X4,multiply(commutator(X4,X3),commutator(X3,multiply(X4,X2))))),
    inference(symmetry,[status(thm)],[c465]) ).

cnf(c467,plain,
    multiply(X4,multiply(commutator(X4,X3),commutator(X3,multiply(X4,X2)))) = multiply(X4,multiply(X4,multiply(commutator(X3,X2),inverse(X4)))),
    inference(congruence,[status(thm)],[c368]) ).

cnf(c468,plain,
    multiply(X3,multiply(X4,multiply(commutator(X4,X3),commutator(X3,multiply(X4,X2))))) = multiply(X3,multiply(X4,multiply(X4,multiply(commutator(X3,X2),inverse(X4))))),
    inference(congruence,[status(thm)],[c467]) ).

cnf(c469,plain,
    multiply(X4,multiply(commutator(X3,X2),inverse(X4))) = multiply(commutator(X3,X2),commutator(X4,commutator(X3,X2))),
    inference(substitution,[status(thm)],[c388]) ).

cnf(c470,plain,
    multiply(X4,multiply(X4,multiply(commutator(X3,X2),inverse(X4)))) = multiply(X4,multiply(commutator(X3,X2),commutator(X4,commutator(X3,X2)))),
    inference(congruence,[status(thm)],[c469]) ).

cnf(c471,plain,
    X2 = inverse(inverse(X2)),
    inference(symmetry,[status(thm)],[c84]) ).

cnf(c472,plain,
    commutator(X3,multiply(X3,X2)) = commutator(inverse(inverse(X3)),multiply(X3,X2)),
    inference(congruence,[status(thm)],[c471]) ).

cnf(c473,plain,
    commutator(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))) = commutator(inverse(inverse(X3)),multiply(X3,X2)),
    inference(substitution,[status(thm)],[c69]) ).

cnf(c474,plain,
    commutator(inverse(inverse(X3)),multiply(X3,X2)) = commutator(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))),
    inference(symmetry,[status(thm)],[c473]) ).

cnf(c475,plain,
    commutator(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))) = commutator(inverse(inverse(X3)),X2),
    inference(congruence,[status(thm)],[c9]) ).

cnf(c476,plain,
    commutator(inverse(inverse(X3)),X2) = commutator(X3,X2),
    inference(congruence,[status(thm)],[c84]) ).

cnf(c477,plain,
    commutator(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))) = commutator(X3,X2),
    inference(transitivity,[status(thm)],[c475,c476]) ).

cnf(c478,plain,
    commutator(inverse(inverse(X3)),multiply(X3,X2)) = commutator(X3,X2),
    inference(transitivity,[status(thm)],[c474,c477]) ).

cnf(c479,plain,
    commutator(X3,multiply(X3,X2)) = commutator(X3,X2),
    inference(transitivity,[status(thm)],[c472,c478]) ).

cnf(c480,plain,
    commutator(X4,multiply(X4,commutator(X3,X2))) = commutator(X4,commutator(X3,X2)),
    inference(substitution,[status(thm)],[c479]) ).

cnf(c481,plain,
    commutator(X4,commutator(X3,X2)) = commutator(X4,multiply(X4,commutator(X3,X2))),
    inference(symmetry,[status(thm)],[c480]) ).

cnf(c482,plain,
    multiply(commutator(X3,X2),commutator(X4,commutator(X3,X2))) = multiply(commutator(X3,X2),commutator(X4,multiply(X4,commutator(X3,X2)))),
    inference(congruence,[status(thm)],[c481]) ).

cnf(c483,plain,
    multiply(X4,multiply(commutator(X3,X2),commutator(X4,commutator(X3,X2)))) = multiply(X4,multiply(commutator(X3,X2),commutator(X4,multiply(X4,commutator(X3,X2))))),
    inference(congruence,[status(thm)],[c482]) ).

cnf(c484,plain,
    multiply(inverse(inverse(X4)),commutator(X3,X2)) = multiply(X4,commutator(X3,X2)),
    inference(substitution,[status(thm)],[c13]) ).

cnf(c485,plain,
    multiply(X4,commutator(X3,X2)) = multiply(inverse(inverse(X4)),commutator(X3,X2)),
    inference(symmetry,[status(thm)],[c484]) ).

cnf(c486,plain,
    commutator(X4,multiply(X4,commutator(X3,X2))) = commutator(X4,multiply(inverse(inverse(X4)),commutator(X3,X2))),
    inference(congruence,[status(thm)],[c485]) ).

cnf(c487,plain,
    multiply(commutator(X3,X2),commutator(X4,multiply(X4,commutator(X3,X2)))) = multiply(commutator(X3,X2),commutator(X4,multiply(inverse(inverse(X4)),commutator(X3,X2)))),
    inference(congruence,[status(thm)],[c486]) ).

cnf(c488,plain,
    multiply(X4,multiply(commutator(X3,X2),commutator(X4,multiply(X4,commutator(X3,X2))))) = multiply(X4,multiply(commutator(X3,X2),commutator(X4,multiply(inverse(inverse(X4)),commutator(X3,X2))))),
    inference(congruence,[status(thm)],[c487]) ).

cnf(c489,plain,
    multiply(inverse(inverse(X4)),multiply(commutator(X3,X2),commutator(X4,multiply(inverse(inverse(X4)),commutator(X3,X2))))) = multiply(X4,multiply(commutator(X3,X2),commutator(X4,multiply(inverse(inverse(X4)),commutator(X3,X2))))),
    inference(substitution,[status(thm)],[c13]) ).

cnf(c490,plain,
    multiply(X4,multiply(commutator(X3,X2),commutator(X4,multiply(inverse(inverse(X4)),commutator(X3,X2))))) = multiply(inverse(inverse(X4)),multiply(commutator(X3,X2),commutator(X4,multiply(inverse(inverse(X4)),commutator(X3,X2))))),
    inference(symmetry,[status(thm)],[c489]) ).

cnf(c491,plain,
    multiply(inverse(inverse(X4)),multiply(commutator(X3,X2),commutator(X4,multiply(inverse(inverse(X4)),commutator(X3,X2))))) = multiply(X4,multiply(inverse(inverse(X4)),multiply(commutator(X3,X2),inverse(X4)))),
    inference(substitution,[status(thm)],[c448]) ).

cnf(c492,plain,
    commutator(commutator(X3,X2),X4) = commutator(X3,commutator(X2,X4)),
    inference(substitution,[status(thm)],[c29]) ).

cnf(c493,plain,
    commutator(X3,commutator(X2,X4)) = commutator(commutator(X3,X2),X4),
    inference(symmetry,[status(thm)],[c492]) ).

cnf(c494,plain,
    multiply(commutator(X3,X2),commutator(X3,commutator(X2,X4))) = multiply(commutator(X3,X2),commutator(commutator(X3,X2),X4)),
    inference(congruence,[status(thm)],[c493]) ).

cnf(c495,plain,
    multiply(inverse(X4),multiply(commutator(X3,X2),X4)) = multiply(commutator(X3,X2),commutator(commutator(X3,X2),X4)),
    inference(substitution,[status(thm)],[c109]) ).

cnf(c496,plain,
    multiply(commutator(X3,X2),commutator(commutator(X3,X2),X4)) = multiply(inverse(X4),multiply(commutator(X3,X2),X4)),
    inference(symmetry,[status(thm)],[c495]) ).

cnf(c497,plain,
    multiply(commutator(X3,X2),commutator(X3,commutator(X2,X4))) = multiply(inverse(X4),multiply(commutator(X3,X2),X4)),
    inference(transitivity,[status(thm)],[c494,c496]) ).

cnf(c498,plain,
    multiply(inverse(X4),multiply(commutator(X3,X2),X4)) = multiply(commutator(X3,X2),commutator(X3,commutator(X2,X4))),
    inference(symmetry,[status(thm)],[c497]) ).

cnf(c499,plain,
    commutator(X4,commutator(X3,X2)) = commutator(X4,commutator(X3,inverse(X2))),
    inference(symmetry,[status(thm)],[c218]) ).

cnf(c500,plain,
    multiply(commutator(X4,X3),commutator(X4,commutator(X3,X2))) = multiply(commutator(X4,X3),commutator(X4,commutator(X3,inverse(X2)))),
    inference(congruence,[status(thm)],[c499]) ).

cnf(c501,plain,
    multiply(commutator(X4,X3),commutator(X4,commutator(X3,inverse(X2)))) = multiply(inverse(inverse(X2)),multiply(commutator(X4,X3),inverse(X2))),
    inference(substitution,[status(thm)],[c497]) ).

cnf(c502,plain,
    multiply(inverse(inverse(X2)),multiply(commutator(X4,X3),inverse(X2))) = multiply(X2,multiply(commutator(X4,X3),inverse(X2))),
    inference(congruence,[status(thm)],[c84]) ).

cnf(c503,plain,
    multiply(commutator(X4,X3),commutator(X4,commutator(X3,inverse(X2)))) = multiply(X2,multiply(commutator(X4,X3),inverse(X2))),
    inference(transitivity,[status(thm)],[c501,c502]) ).

cnf(c504,plain,
    multiply(commutator(X4,X3),commutator(X4,commutator(X3,X2))) = multiply(X2,multiply(commutator(X4,X3),inverse(X2))),
    inference(transitivity,[status(thm)],[c500,c503]) ).

cnf(c505,plain,
    multiply(commutator(X3,X2),commutator(X3,commutator(X2,X4))) = multiply(X4,multiply(commutator(X3,X2),inverse(X4))),
    inference(substitution,[status(thm)],[c504]) ).

cnf(c506,plain,
    multiply(inverse(X4),multiply(commutator(X3,X2),X4)) = multiply(X4,multiply(commutator(X3,X2),inverse(X4))),
    inference(transitivity,[status(thm)],[c498,c505]) ).

cnf(c507,plain,
    multiply(inverse(inverse(X4)),multiply(commutator(X3,X2),inverse(X4))) = multiply(inverse(X4),multiply(commutator(X3,X2),inverse(inverse(X4)))),
    inference(substitution,[status(thm)],[c506]) ).

cnf(c508,plain,
    multiply(X4,multiply(inverse(inverse(X4)),multiply(commutator(X3,X2),inverse(X4)))) = multiply(X4,multiply(inverse(X4),multiply(commutator(X3,X2),inverse(inverse(X4))))),
    inference(congruence,[status(thm)],[c507]) ).

cnf(c509,plain,
    multiply(X4,multiply(inverse(X4),multiply(commutator(X3,X2),inverse(inverse(X4))))) = multiply(commutator(X3,X2),inverse(inverse(X4))),
    inference(substitution,[status(thm)],[c26]) ).

cnf(c510,plain,
    multiply(commutator(X3,X2),inverse(inverse(X4))) = multiply(commutator(X3,X2),X4),
    inference(congruence,[status(thm)],[c84]) ).

cnf(c511,plain,
    multiply(X4,multiply(inverse(X4),multiply(commutator(X3,X2),inverse(inverse(X4))))) = multiply(commutator(X3,X2),X4),
    inference(transitivity,[status(thm)],[c509,c510]) ).

cnf(c512,plain,
    multiply(X4,multiply(inverse(inverse(X4)),multiply(commutator(X3,X2),inverse(X4)))) = multiply(commutator(X3,X2),X4),
    inference(transitivity,[status(thm)],[c508,c511]) ).

cnf(c513,plain,
    multiply(inverse(inverse(X4)),multiply(commutator(X3,X2),commutator(X4,multiply(inverse(inverse(X4)),commutator(X3,X2))))) = multiply(commutator(X3,X2),X4),
    inference(transitivity,[status(thm)],[c491,c512]) ).

cnf(c514,plain,
    multiply(X4,multiply(commutator(X3,X2),commutator(X4,multiply(inverse(inverse(X4)),commutator(X3,X2))))) = multiply(commutator(X3,X2),X4),
    inference(transitivity,[status(thm)],[c490,c513]) ).

cnf(c515,plain,
    multiply(X4,multiply(commutator(X3,X2),commutator(X4,multiply(X4,commutator(X3,X2))))) = multiply(commutator(X3,X2),X4),
    inference(transitivity,[status(thm)],[c488,c514]) ).

cnf(c516,plain,
    multiply(X4,multiply(commutator(X3,X2),commutator(X4,commutator(X3,X2)))) = multiply(commutator(X3,X2),X4),
    inference(transitivity,[status(thm)],[c483,c515]) ).

cnf(c517,plain,
    multiply(X4,multiply(X4,multiply(commutator(X3,X2),inverse(X4)))) = multiply(commutator(X3,X2),X4),
    inference(transitivity,[status(thm)],[c470,c516]) ).

cnf(c518,plain,
    multiply(X3,multiply(X4,multiply(X4,multiply(commutator(X3,X2),inverse(X4))))) = multiply(X3,multiply(commutator(X3,X2),X4)),
    inference(congruence,[status(thm)],[c517]) ).

cnf(c519,plain,
    multiply(X3,multiply(X4,multiply(commutator(X4,X3),commutator(X3,multiply(X4,X2))))) = multiply(X3,multiply(commutator(X3,X2),X4)),
    inference(transitivity,[status(thm)],[c468,c518]) ).

cnf(c520,plain,
    multiply(X4,multiply(X3,commutator(X3,multiply(X4,X2)))) = multiply(X3,multiply(commutator(X3,X2),X4)),
    inference(transitivity,[status(thm)],[c466,c519]) ).

cnf(c521,plain,
    multiply(X3,multiply(commutator(X3,X2),X4)) = multiply(X4,multiply(X3,commutator(X3,multiply(X4,X2)))),
    inference(symmetry,[status(thm)],[c520]) ).

cnf(c522,plain,
    multiply(inverse(X4),multiply(X3,multiply(commutator(X3,X2),X4))) = multiply(inverse(X4),multiply(X4,multiply(X3,commutator(X3,multiply(X4,X2))))),
    inference(congruence,[status(thm)],[c521]) ).

cnf(c523,plain,
    multiply(inverse(X4),multiply(X4,multiply(X3,commutator(X3,multiply(X4,X2))))) = multiply(X3,commutator(X3,multiply(X4,X2))),
    inference(substitution,[status(thm)],[c9]) ).

cnf(c524,plain,
    multiply(inverse(X4),multiply(X3,multiply(commutator(X3,X2),X4))) = multiply(X3,commutator(X3,multiply(X4,X2))),
    inference(transitivity,[status(thm)],[c522,c523]) ).

cnf(c525,plain,
    multiply(inverse(multiply(X3,inverse(X4))),multiply(X4,multiply(commutator(X4,X2),multiply(X3,inverse(X4))))) = multiply(X4,commutator(X4,multiply(multiply(X3,inverse(X4)),X2))),
    inference(substitution,[status(thm)],[c524]) ).

cnf(c526,plain,
    multiply(multiply(X3,inverse(X4)),X2) = multiply(X3,multiply(inverse(X4),X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c527,plain,
    commutator(X4,multiply(multiply(X3,inverse(X4)),X2)) = commutator(X4,multiply(X3,multiply(inverse(X4),X2))),
    inference(congruence,[status(thm)],[c526]) ).

cnf(c528,plain,
    multiply(X4,commutator(X4,multiply(multiply(X3,inverse(X4)),X2))) = multiply(X4,commutator(X4,multiply(X3,multiply(inverse(X4),X2)))),
    inference(congruence,[status(thm)],[c527]) ).

cnf(c529,plain,
    multiply(inverse(inverse(X3)),multiply(X4,X2)) = multiply(X3,multiply(X4,X2)),
    inference(substitution,[status(thm)],[c13]) ).

cnf(c530,plain,
    multiply(X3,multiply(X4,X2)) = multiply(inverse(inverse(X3)),multiply(X4,X2)),
    inference(symmetry,[status(thm)],[c529]) ).

cnf(c531,plain,
    commutator(X4,multiply(X3,multiply(X4,X2))) = commutator(X4,multiply(inverse(inverse(X3)),multiply(X4,X2))),
    inference(congruence,[status(thm)],[c530]) ).

cnf(c532,plain,
    X2 = multiply(inverse(X3),multiply(X3,X2)),
    inference(symmetry,[status(thm)],[c9]) ).

cnf(c533,plain,
    multiply(X4,X2) = multiply(X4,multiply(inverse(X3),multiply(X3,X2))),
    inference(congruence,[status(thm)],[c532]) ).

cnf(c534,plain,
    multiply(inverse(inverse(X3)),multiply(X4,X2)) = multiply(inverse(inverse(X3)),multiply(X4,multiply(inverse(X3),multiply(X3,X2)))),
    inference(congruence,[status(thm)],[c533]) ).

cnf(c535,plain,
    commutator(X4,multiply(inverse(inverse(X3)),multiply(X4,X2))) = commutator(X4,multiply(inverse(inverse(X3)),multiply(X4,multiply(inverse(X3),multiply(X3,X2))))),
    inference(congruence,[status(thm)],[c534]) ).

cnf(c536,plain,
    multiply(inverse(X3),multiply(X4,multiply(X3,X2))) = multiply(X4,multiply(commutator(X4,X3),X2)),
    inference(substitution,[status(thm)],[c346]) ).

cnf(c537,plain,
    commutator(X4,multiply(inverse(X3),multiply(X4,multiply(X3,X2)))) = commutator(X4,multiply(X4,multiply(commutator(X4,X3),X2))),
    inference(congruence,[status(thm)],[c536]) ).

cnf(c538,plain,
    commutator(X4,multiply(X4,multiply(commutator(X4,X3),X2))) = commutator(X4,multiply(commutator(X4,X3),X2)),
    inference(substitution,[status(thm)],[c479]) ).

cnf(c539,plain,
    commutator(X4,multiply(inverse(X3),multiply(X4,multiply(X3,X2)))) = commutator(X4,multiply(commutator(X4,X3),X2)),
    inference(transitivity,[status(thm)],[c537,c538]) ).

cnf(c540,plain,
    commutator(X4,multiply(inverse(inverse(X3)),multiply(X4,multiply(inverse(X3),multiply(X3,X2))))) = commutator(X4,multiply(commutator(X4,inverse(X3)),multiply(X3,X2))),
    inference(substitution,[status(thm)],[c539]) ).

cnf(c541,plain,
    multiply(inverse(X2),multiply(X2,commutator(X4,multiply(commutator(X4,X3),X2)))) = commutator(X4,multiply(commutator(X4,X3),X2)),
    inference(substitution,[status(thm)],[c9]) ).

cnf(c542,plain,
    commutator(X4,multiply(commutator(X4,X3),X2)) = multiply(inverse(X2),multiply(X2,commutator(X4,multiply(commutator(X4,X3),X2)))),
    inference(symmetry,[status(thm)],[c541]) ).

cnf(c543,plain,
    commutator(X3,multiply(inverse(X2),multiply(X3,multiply(X2,X4)))) = commutator(X3,multiply(commutator(X3,X2),X4)),
    inference(substitution,[status(thm)],[c539]) ).

cnf(c544,plain,
    commutator(X3,multiply(commutator(X3,X2),X4)) = commutator(X3,multiply(inverse(X2),multiply(X3,multiply(X2,X4)))),
    inference(symmetry,[status(thm)],[c543]) ).

cnf(c545,plain,
    multiply(X4,commutator(X3,multiply(commutator(X3,X2),X4))) = multiply(X4,commutator(X3,multiply(inverse(X2),multiply(X3,multiply(X2,X4))))),
    inference(congruence,[status(thm)],[c544]) ).

cnf(c546,plain,
    multiply(multiply(X3,X2),X4) = multiply(X3,multiply(X2,X4)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c547,plain,
    multiply(X3,multiply(X2,X4)) = multiply(multiply(X3,X2),X4),
    inference(symmetry,[status(thm)],[c546]) ).

cnf(c548,plain,
    multiply(inverse(X2),multiply(X3,multiply(X2,X4))) = multiply(inverse(X2),multiply(multiply(X3,X2),X4)),
    inference(congruence,[status(thm)],[c547]) ).

cnf(c549,plain,
    commutator(X3,multiply(inverse(X2),multiply(X3,multiply(X2,X4)))) = commutator(X3,multiply(inverse(X2),multiply(multiply(X3,X2),X4))),
    inference(congruence,[status(thm)],[c548]) ).

cnf(c550,plain,
    multiply(X4,commutator(X3,multiply(inverse(X2),multiply(X3,multiply(X2,X4))))) = multiply(X4,commutator(X3,multiply(inverse(X2),multiply(multiply(X3,X2),X4)))),
    inference(congruence,[status(thm)],[c549]) ).

cnf(c551,plain,
    multiply(multiply(inverse(X2),multiply(X3,X2)),X4) = multiply(inverse(X2),multiply(multiply(X3,X2),X4)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c552,plain,
    multiply(inverse(X2),multiply(multiply(X3,X2),X4)) = multiply(multiply(inverse(X2),multiply(X3,X2)),X4),
    inference(symmetry,[status(thm)],[c551]) ).

cnf(c553,plain,
    commutator(X3,multiply(inverse(X2),multiply(multiply(X3,X2),X4))) = commutator(X3,multiply(multiply(inverse(X2),multiply(X3,X2)),X4)),
    inference(congruence,[status(thm)],[c552]) ).

cnf(c554,plain,
    multiply(X4,commutator(X3,multiply(inverse(X2),multiply(multiply(X3,X2),X4)))) = multiply(X4,commutator(X3,multiply(multiply(inverse(X2),multiply(X3,X2)),X4))),
    inference(congruence,[status(thm)],[c553]) ).

cnf(c555,plain,
    multiply(X3,multiply(commutator(X3,multiply(inverse(X2),multiply(X3,X2))),multiply(X4,inverse(X3)))) = multiply(X4,commutator(X3,multiply(multiply(inverse(X2),multiply(X3,X2)),X4))),
    inference(substitution,[status(thm)],[c454]) ).

cnf(c556,plain,
    multiply(X4,commutator(X3,multiply(multiply(inverse(X2),multiply(X3,X2)),X4))) = multiply(X3,multiply(commutator(X3,multiply(inverse(X2),multiply(X3,X2))),multiply(X4,inverse(X3)))),
    inference(symmetry,[status(thm)],[c555]) ).

cnf(c557,plain,
    multiply(inverse(X2),multiply(X3,X2)) = multiply(X3,commutator(X3,X2)),
    inference(substitution,[status(thm)],[c109]) ).

cnf(c558,plain,
    commutator(X3,multiply(inverse(X2),multiply(X3,X2))) = commutator(X3,multiply(X3,commutator(X3,X2))),
    inference(congruence,[status(thm)],[c557]) ).

cnf(c559,plain,
    commutator(X3,multiply(X3,commutator(X3,X2))) = commutator(X3,commutator(X3,X2)),
    inference(substitution,[status(thm)],[c479]) ).

cnf(c560,plain,
    commutator(X3,multiply(X3,commutator(X3,X2))) = identity,
    inference(transitivity,[status(thm)],[c559,c156]) ).

cnf(c561,plain,
    commutator(X3,multiply(inverse(X2),multiply(X3,X2))) = identity,
    inference(transitivity,[status(thm)],[c558,c560]) ).

cnf(c562,plain,
    multiply(commutator(X3,multiply(inverse(X2),multiply(X3,X2))),multiply(X4,inverse(X3))) = multiply(identity,multiply(X4,inverse(X3))),
    inference(congruence,[status(thm)],[c561]) ).

cnf(c563,plain,
    multiply(X3,multiply(commutator(X3,multiply(inverse(X2),multiply(X3,X2))),multiply(X4,inverse(X3)))) = multiply(X3,multiply(identity,multiply(X4,inverse(X3)))),
    inference(congruence,[status(thm)],[c562]) ).

cnf(c564,plain,
    multiply(identity,multiply(X3,inverse(X2))) = multiply(X3,inverse(X2)),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c565,plain,
    multiply(X2,multiply(identity,multiply(X3,inverse(X2)))) = multiply(X2,multiply(X3,inverse(X2))),
    inference(congruence,[status(thm)],[c564]) ).

cnf(c566,plain,
    multiply(X3,multiply(commutator(X3,multiply(inverse(X2),multiply(X3,X2))),multiply(X4,inverse(X3)))) = multiply(X3,multiply(X4,inverse(X3))),
    inference(transitivity,[status(thm)],[c563,c565]) ).

cnf(c567,plain,
    multiply(X4,commutator(X3,multiply(multiply(inverse(X2),multiply(X3,X2)),X4))) = multiply(X3,multiply(X4,inverse(X3))),
    inference(transitivity,[status(thm)],[c556,c566]) ).

cnf(c568,plain,
    multiply(X4,commutator(X3,multiply(inverse(X2),multiply(multiply(X3,X2),X4)))) = multiply(X3,multiply(X4,inverse(X3))),
    inference(transitivity,[status(thm)],[c554,c567]) ).

cnf(c569,plain,
    multiply(X4,commutator(X3,multiply(inverse(X2),multiply(X3,multiply(X2,X4))))) = multiply(X3,multiply(X4,inverse(X3))),
    inference(transitivity,[status(thm)],[c550,c568]) ).

cnf(c570,plain,
    multiply(X4,commutator(X3,multiply(commutator(X3,X2),X4))) = multiply(X3,multiply(X4,inverse(X3))),
    inference(transitivity,[status(thm)],[c545,c569]) ).

cnf(c571,plain,
    multiply(X2,commutator(X4,multiply(commutator(X4,X3),X2))) = multiply(X4,multiply(X2,inverse(X4))),
    inference(substitution,[status(thm)],[c570]) ).

cnf(c572,plain,
    multiply(inverse(X2),multiply(X2,commutator(X4,multiply(commutator(X4,X3),X2)))) = multiply(inverse(X2),multiply(X4,multiply(X2,inverse(X4)))),
    inference(congruence,[status(thm)],[c571]) ).

cnf(c573,plain,
    multiply(inverse(X2),multiply(X3,multiply(X2,inverse(X3)))) = commutator(X2,inverse(X3)),
    inference(substitution,[status(thm)],[c316]) ).

cnf(c574,plain,
    multiply(inverse(X2),multiply(X3,multiply(X2,inverse(X3)))) = commutator(X3,X2),
    inference(transitivity,[status(thm)],[c573,c199]) ).

cnf(c575,plain,
    multiply(inverse(X2),multiply(X2,commutator(X4,multiply(commutator(X4,X3),X2)))) = commutator(X4,X2),
    inference(transitivity,[status(thm)],[c572,c574]) ).

cnf(c576,plain,
    commutator(X4,multiply(commutator(X4,X3),X2)) = commutator(X4,X2),
    inference(transitivity,[status(thm)],[c542,c575]) ).

cnf(c577,plain,
    commutator(X4,multiply(commutator(X4,inverse(X3)),multiply(X3,X2))) = commutator(X4,multiply(X3,X2)),
    inference(substitution,[status(thm)],[c576]) ).

cnf(c578,plain,
    commutator(X4,multiply(inverse(inverse(X3)),multiply(X4,multiply(inverse(X3),multiply(X3,X2))))) = commutator(X4,multiply(X3,X2)),
    inference(transitivity,[status(thm)],[c540,c577]) ).

cnf(c579,plain,
    commutator(X4,multiply(inverse(inverse(X3)),multiply(X4,X2))) = commutator(X4,multiply(X3,X2)),
    inference(transitivity,[status(thm)],[c535,c578]) ).

cnf(c580,plain,
    commutator(X4,multiply(X3,multiply(X4,X2))) = commutator(X4,multiply(X3,X2)),
    inference(transitivity,[status(thm)],[c531,c579]) ).

cnf(c581,plain,
    commutator(X4,multiply(X3,multiply(X4,multiply(inverse(X4),X2)))) = commutator(X4,multiply(X3,multiply(inverse(X4),X2))),
    inference(substitution,[status(thm)],[c580]) ).

cnf(c582,plain,
    commutator(X4,multiply(X3,multiply(inverse(X4),X2))) = commutator(X4,multiply(X3,multiply(X4,multiply(inverse(X4),X2)))),
    inference(symmetry,[status(thm)],[c581]) ).

cnf(c583,plain,
    multiply(X3,multiply(X4,multiply(inverse(X4),X2))) = multiply(X3,X2),
    inference(congruence,[status(thm)],[c26]) ).

cnf(c584,plain,
    commutator(X4,multiply(X3,multiply(X4,multiply(inverse(X4),X2)))) = commutator(X4,multiply(X3,X2)),
    inference(congruence,[status(thm)],[c583]) ).

cnf(c585,plain,
    commutator(X4,multiply(X3,multiply(inverse(X4),X2))) = commutator(X4,multiply(X3,X2)),
    inference(transitivity,[status(thm)],[c582,c584]) ).

cnf(c586,plain,
    multiply(X4,commutator(X4,multiply(X3,multiply(inverse(X4),X2)))) = multiply(X4,commutator(X4,multiply(X3,X2))),
    inference(congruence,[status(thm)],[c585]) ).

cnf(c587,plain,
    multiply(X4,commutator(X4,multiply(multiply(X3,inverse(X4)),X2))) = multiply(X4,commutator(X4,multiply(X3,X2))),
    inference(transitivity,[status(thm)],[c528,c586]) ).

cnf(c588,plain,
    multiply(inverse(multiply(X3,inverse(X4))),multiply(X4,multiply(commutator(X4,X2),multiply(X3,inverse(X4))))) = multiply(X4,commutator(X4,multiply(X3,X2))),
    inference(transitivity,[status(thm)],[c525,c587]) ).

cnf(c589,plain,
    multiply(inverse(multiply(X3,inverse(X4))),multiply(X3,commutator(X4,multiply(X2,X3)))) = multiply(X4,commutator(X4,multiply(X3,X2))),
    inference(transitivity,[status(thm)],[c457,c588]) ).

cnf(c590,plain,
    multiply(multiply(inverse(inverse(X4)),inverse(X3)),multiply(X3,commutator(X4,multiply(X2,X3)))) = multiply(X4,commutator(X4,multiply(X3,X2))),
    inference(transitivity,[status(thm)],[c403,c589]) ).

cnf(c591,plain,
    multiply(inverse(inverse(X4)),multiply(inverse(X3),multiply(X3,commutator(X4,multiply(X2,X3))))) = multiply(X4,commutator(X4,multiply(X3,X2))),
    inference(transitivity,[status(thm)],[c400,c590]) ).

cnf(c592,plain,
    multiply(X4,multiply(inverse(X3),multiply(X3,commutator(X4,multiply(X2,X3))))) = multiply(X4,commutator(X4,multiply(X3,X2))),
    inference(transitivity,[status(thm)],[c398,c591]) ).

cnf(c593,plain,
    multiply(X4,commutator(X4,multiply(X2,X3))) = multiply(X4,commutator(X4,multiply(X3,X2))),
    inference(transitivity,[status(thm)],[c396,c592]) ).

cnf(c594,plain,
    multiply(inverse(X4),multiply(X4,commutator(X4,multiply(X2,X3)))) = multiply(inverse(X4),multiply(X4,commutator(X4,multiply(X3,X2)))),
    inference(congruence,[status(thm)],[c593]) ).

cnf(c595,plain,
    multiply(inverse(X4),multiply(X4,commutator(X4,multiply(X3,X2)))) = commutator(X4,multiply(X3,X2)),
    inference(substitution,[status(thm)],[c9]) ).

cnf(c596,plain,
    multiply(inverse(X4),multiply(X4,commutator(X4,multiply(X2,X3)))) = commutator(X4,multiply(X3,X2)),
    inference(transitivity,[status(thm)],[c594,c595]) ).

cnf(c597,plain,
    commutator(X4,multiply(X2,X3)) = commutator(X4,multiply(X3,X2)),
    inference(transitivity,[status(thm)],[c393,c596]) ).

cnf(c598,plain,
    commutator(X4,multiply(multiply(X3,inverse(X2)),X2)) = commutator(X4,multiply(X2,multiply(X3,inverse(X2)))),
    inference(substitution,[status(thm)],[c597]) ).

cnf(c599,plain,
    commutator(X4,multiply(X2,multiply(X3,inverse(X2)))) = commutator(X4,multiply(multiply(X3,inverse(X2)),X2)),
    inference(symmetry,[status(thm)],[c598]) ).

cnf(c600,plain,
    multiply(multiply(X3,inverse(X2)),X2) = multiply(X3,multiply(inverse(X2),X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c601,plain,
    commutator(X4,multiply(multiply(X3,inverse(X2)),X2)) = commutator(X4,multiply(X3,multiply(inverse(X2),X2))),
    inference(congruence,[status(thm)],[c600]) ).

cnf(c602,plain,
    multiply(X3,multiply(inverse(X2),X2)) = multiply(X3,identity),
    inference(congruence,[status(thm)],[c5]) ).

cnf(c603,plain,
    commutator(X4,multiply(X3,multiply(inverse(X2),X2))) = commutator(X4,multiply(X3,identity)),
    inference(congruence,[status(thm)],[c602]) ).

cnf(c604,plain,
    commutator(X3,multiply(X2,identity)) = commutator(X3,X2),
    inference(congruence,[status(thm)],[c20]) ).

cnf(c605,plain,
    commutator(X4,multiply(X3,multiply(inverse(X2),X2))) = commutator(X4,X3),
    inference(transitivity,[status(thm)],[c603,c604]) ).

cnf(c606,plain,
    commutator(X4,multiply(multiply(X3,inverse(X2)),X2)) = commutator(X4,X3),
    inference(transitivity,[status(thm)],[c601,c605]) ).

cnf(c607,plain,
    commutator(X4,multiply(X2,multiply(X3,inverse(X2)))) = commutator(X4,X3),
    inference(transitivity,[status(thm)],[c599,c606]) ).

cnf(c608,plain,
    commutator(X4,multiply(X3,commutator(X2,X3))) = commutator(X4,X3),
    inference(transitivity,[status(thm)],[c391,c607]) ).

cnf(c609,plain,
    commutator(X3,multiply(X2,commutator(X4,X2))) = commutator(X3,X2),
    inference(substitution,[status(thm)],[c608]) ).

cnf(c610,plain,
    multiply(commutator(X2,X3),commutator(X3,multiply(X2,commutator(X4,X2)))) = multiply(commutator(X2,X3),commutator(X3,X2)),
    inference(congruence,[status(thm)],[c609]) ).

cnf(c611,plain,
    multiply(inverse(X3),multiply(X3,commutator(X2,X3))) = commutator(X2,X3),
    inference(substitution,[status(thm)],[c9]) ).

cnf(c612,plain,
    commutator(X2,X3) = multiply(inverse(X3),multiply(X3,commutator(X2,X3))),
    inference(symmetry,[status(thm)],[c611]) ).

cnf(c613,plain,
    multiply(commutator(X3,X2),commutator(X2,X3)) = multiply(commutator(X3,X2),multiply(inverse(X3),multiply(X3,commutator(X2,X3)))),
    inference(congruence,[status(thm)],[c612]) ).

cnf(c614,plain,
    multiply(commutator(X2,X3),X3) = multiply(X3,commutator(X2,X3)),
    inference(substitution,[status(thm)],[c256]) ).

cnf(c615,plain,
    multiply(X3,commutator(X2,X3)) = multiply(commutator(X2,X3),X3),
    inference(symmetry,[status(thm)],[c614]) ).

cnf(c616,plain,
    multiply(inverse(X3),multiply(X3,commutator(X2,X3))) = multiply(inverse(X3),multiply(commutator(X2,X3),X3)),
    inference(congruence,[status(thm)],[c615]) ).

cnf(c617,plain,
    multiply(commutator(X3,X2),multiply(inverse(X3),multiply(X3,commutator(X2,X3)))) = multiply(commutator(X3,X2),multiply(inverse(X3),multiply(commutator(X2,X3),X3))),
    inference(congruence,[status(thm)],[c616]) ).

cnf(c618,plain,
    X2 = inverse(inverse(X2)),
    inference(symmetry,[status(thm)],[c84]) ).

cnf(c619,plain,
    multiply(commutator(X2,X3),X3) = multiply(commutator(X2,X3),inverse(inverse(X3))),
    inference(congruence,[status(thm)],[c618]) ).

cnf(c620,plain,
    multiply(inverse(X3),multiply(commutator(X2,X3),X3)) = multiply(inverse(X3),multiply(commutator(X2,X3),inverse(inverse(X3)))),
    inference(congruence,[status(thm)],[c619]) ).

cnf(c621,plain,
    multiply(commutator(X3,X2),multiply(inverse(X3),multiply(commutator(X2,X3),X3))) = multiply(commutator(X3,X2),multiply(inverse(X3),multiply(commutator(X2,X3),inverse(inverse(X3))))),
    inference(congruence,[status(thm)],[c620]) ).

cnf(c622,plain,
    commutator(X2,X3) = inverse(commutator(X3,X2)),
    inference(symmetry,[status(thm)],[c97]) ).

cnf(c623,plain,
    multiply(commutator(X2,X3),inverse(inverse(X3))) = multiply(inverse(commutator(X3,X2)),inverse(inverse(X3))),
    inference(congruence,[status(thm)],[c622]) ).

cnf(c624,plain,
    multiply(inverse(X3),multiply(commutator(X2,X3),inverse(inverse(X3)))) = multiply(inverse(X3),multiply(inverse(commutator(X3,X2)),inverse(inverse(X3)))),
    inference(congruence,[status(thm)],[c623]) ).

cnf(c625,plain,
    multiply(commutator(X3,X2),multiply(inverse(X3),multiply(commutator(X2,X3),inverse(inverse(X3))))) = multiply(commutator(X3,X2),multiply(inverse(X3),multiply(inverse(commutator(X3,X2)),inverse(inverse(X3))))),
    inference(congruence,[status(thm)],[c624]) ).

cnf(c626,plain,
    inverse(multiply(inverse(X3),commutator(X3,X2))) = multiply(inverse(commutator(X3,X2)),inverse(inverse(X3))),
    inference(substitution,[status(thm)],[c61]) ).

cnf(c627,plain,
    multiply(inverse(commutator(X3,X2)),inverse(inverse(X3))) = inverse(multiply(inverse(X3),commutator(X3,X2))),
    inference(symmetry,[status(thm)],[c626]) ).

cnf(c628,plain,
    multiply(inverse(X3),multiply(inverse(commutator(X3,X2)),inverse(inverse(X3)))) = multiply(inverse(X3),inverse(multiply(inverse(X3),commutator(X3,X2)))),
    inference(congruence,[status(thm)],[c627]) ).

cnf(c629,plain,
    multiply(commutator(X3,X2),multiply(inverse(X3),multiply(inverse(commutator(X3,X2)),inverse(inverse(X3))))) = multiply(commutator(X3,X2),multiply(inverse(X3),inverse(multiply(inverse(X3),commutator(X3,X2))))),
    inference(congruence,[status(thm)],[c628]) ).

cnf(c630,plain,
    multiply(inverse(X2),identity) = inverse(X2),
    inference(substitution,[status(thm)],[c20]) ).

cnf(c631,plain,
    inverse(X2) = multiply(inverse(X2),identity),
    inference(symmetry,[status(thm)],[c630]) ).

cnf(c632,plain,
    multiply(commutator(X3,X2),inverse(X3)) = multiply(commutator(X3,X2),multiply(inverse(X3),identity)),
    inference(congruence,[status(thm)],[c631]) ).

cnf(c633,plain,
    commutator(commutator(inverse(X3),X3),X2) = commutator(inverse(X3),commutator(X3,X2)),
    inference(substitution,[status(thm)],[c29]) ).

cnf(c634,plain,
    commutator(inverse(X3),commutator(X3,X2)) = commutator(commutator(inverse(X3),X3),X2),
    inference(symmetry,[status(thm)],[c633]) ).

cnf(c635,plain,
    commutator(inverse(X2),X2) = multiply(inverse(inverse(X2)),multiply(inverse(X2),multiply(inverse(X2),X2))),
    inference(substitution,[status(thm)],[c34]) ).

cnf(c636,plain,
    multiply(inverse(inverse(X2)),multiply(inverse(X2),multiply(inverse(X2),X2))) = multiply(inverse(X2),X2),
    inference(substitution,[status(thm)],[c9]) ).

cnf(c637,plain,
    multiply(inverse(inverse(X2)),multiply(inverse(X2),multiply(inverse(X2),X2))) = identity,
    inference(transitivity,[status(thm)],[c636,c5]) ).

cnf(c638,plain,
    commutator(inverse(X2),X2) = identity,
    inference(transitivity,[status(thm)],[c635,c637]) ).

cnf(c639,plain,
    commutator(commutator(inverse(X3),X3),X2) = commutator(identity,X2),
    inference(congruence,[status(thm)],[c638]) ).

cnf(c640,plain,
    commutator(commutator(inverse(X3),X3),X2) = identity,
    inference(transitivity,[status(thm)],[c639,c154]) ).

cnf(c641,plain,
    commutator(inverse(X3),commutator(X3,X2)) = identity,
    inference(transitivity,[status(thm)],[c634,c640]) ).

cnf(c642,plain,
    identity = commutator(inverse(X3),commutator(X3,X2)),
    inference(symmetry,[status(thm)],[c641]) ).

cnf(c643,plain,
    multiply(inverse(X3),identity) = multiply(inverse(X3),commutator(inverse(X3),commutator(X3,X2))),
    inference(congruence,[status(thm)],[c642]) ).

cnf(c644,plain,
    multiply(commutator(X3,X2),multiply(inverse(X3),identity)) = multiply(commutator(X3,X2),multiply(inverse(X3),commutator(inverse(X3),commutator(X3,X2)))),
    inference(congruence,[status(thm)],[c643]) ).

cnf(c645,plain,
    multiply(commutator(X3,X2),multiply(inverse(X3),commutator(inverse(X3),commutator(X3,X2)))) = multiply(inverse(X3),commutator(X3,X2)),
    inference(substitution,[status(thm)],[c132]) ).

cnf(c646,plain,
    multiply(commutator(X3,X2),multiply(inverse(X3),identity)) = multiply(inverse(X3),commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c644,c645]) ).

cnf(c647,plain,
    multiply(commutator(X3,X2),inverse(X3)) = multiply(inverse(X3),commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c632,c646]) ).

cnf(c648,plain,
    multiply(inverse(X3),commutator(X3,X2)) = multiply(commutator(X3,X2),inverse(X3)),
    inference(symmetry,[status(thm)],[c647]) ).

cnf(c649,plain,
    inverse(multiply(inverse(X3),commutator(X3,X2))) = inverse(multiply(commutator(X3,X2),inverse(X3))),
    inference(congruence,[status(thm)],[c648]) ).

cnf(c650,plain,
    multiply(inverse(X3),inverse(multiply(inverse(X3),commutator(X3,X2)))) = multiply(inverse(X3),inverse(multiply(commutator(X3,X2),inverse(X3)))),
    inference(congruence,[status(thm)],[c649]) ).

cnf(c651,plain,
    multiply(commutator(X3,X2),multiply(inverse(X3),inverse(multiply(inverse(X3),commutator(X3,X2))))) = multiply(commutator(X3,X2),multiply(inverse(X3),inverse(multiply(commutator(X3,X2),inverse(X3))))),
    inference(congruence,[status(thm)],[c650]) ).

cnf(c652,plain,
    multiply(commutator(X3,X2),multiply(inverse(X3),inverse(multiply(commutator(X3,X2),inverse(X3))))) = identity,
    inference(substitution,[status(thm)],[c53]) ).

cnf(c653,plain,
    multiply(commutator(X3,X2),multiply(inverse(X3),inverse(multiply(inverse(X3),commutator(X3,X2))))) = identity,
    inference(transitivity,[status(thm)],[c651,c652]) ).

cnf(c654,plain,
    multiply(commutator(X3,X2),multiply(inverse(X3),multiply(inverse(commutator(X3,X2)),inverse(inverse(X3))))) = identity,
    inference(transitivity,[status(thm)],[c629,c653]) ).

cnf(c655,plain,
    multiply(commutator(X3,X2),multiply(inverse(X3),multiply(commutator(X2,X3),inverse(inverse(X3))))) = identity,
    inference(transitivity,[status(thm)],[c625,c654]) ).

cnf(c656,plain,
    multiply(commutator(X3,X2),multiply(inverse(X3),multiply(commutator(X2,X3),X3))) = identity,
    inference(transitivity,[status(thm)],[c621,c655]) ).

cnf(c657,plain,
    multiply(commutator(X3,X2),multiply(inverse(X3),multiply(X3,commutator(X2,X3)))) = identity,
    inference(transitivity,[status(thm)],[c617,c656]) ).

cnf(c658,plain,
    multiply(commutator(X3,X2),commutator(X2,X3)) = identity,
    inference(transitivity,[status(thm)],[c613,c657]) ).

cnf(c659,plain,
    multiply(commutator(X2,X3),commutator(X3,X2)) = identity,
    inference(substitution,[status(thm)],[c658]) ).

cnf(c660,plain,
    multiply(commutator(X2,X3),commutator(X3,multiply(X2,commutator(X4,X2)))) = identity,
    inference(transitivity,[status(thm)],[c610,c659]) ).

cnf(c661,plain,
    multiply(X2,multiply(commutator(X3,commutator(X4,X2)),inverse(X2))) = identity,
    inference(transitivity,[status(thm)],[c370,c660]) ).

cnf(c662,plain,
    multiply(X2,multiply(inverse(X2),commutator(X4,commutator(X3,X2)))) = identity,
    inference(transitivity,[status(thm)],[c284,c661]) ).

cnf(c663,plain,
    commutator(X4,commutator(X3,X2)) = identity,
    inference(transitivity,[status(thm)],[c28,c662]) ).

cnf(c664,plain,
    identity = commutator(X4,commutator(X3,X2)),
    inference(symmetry,[status(thm)],[c663]) ).

cnf(c665,plain,
    multiply(X4,identity) = multiply(X4,commutator(X4,commutator(X3,X2))),
    inference(congruence,[status(thm)],[c664]) ).

cnf(c666,plain,
    multiply(commutator(X3,X2),multiply(X4,identity)) = multiply(commutator(X3,X2),multiply(X4,commutator(X4,commutator(X3,X2)))),
    inference(congruence,[status(thm)],[c665]) ).

cnf(c667,plain,
    multiply(commutator(X3,X2),multiply(X4,commutator(X4,commutator(X3,X2)))) = multiply(X4,commutator(X3,X2)),
    inference(substitution,[status(thm)],[c132]) ).

cnf(c668,plain,
    multiply(commutator(X3,X2),multiply(X4,identity)) = multiply(X4,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c666,c667]) ).

cnf(c669,plain,
    multiply(commutator(X3,X2),X4) = multiply(X4,commutator(X3,X2)),
    inference(transitivity,[status(thm)],[c22,c668]) ).

cnf(c670,plain,
    multiply(commutator(b,c),a) = multiply(a,commutator(b,c)),
    inference(substitution,[status(thm)],[c669]) ).

cnf(c671,plain,
    multiply(a,commutator(b,c)) = multiply(commutator(b,c),a),
    inference(symmetry,[status(thm)],[c670]) ).

cnf(c672,plain,
    $false,
    inference(resolution,[status(thm)],[c1,c671]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : GRP024-5 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35  % Computer : n004.cluster.edu
% 0.09/0.35  % Model    : x86_64 x86_64
% 0.09/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35  % Memory   : 8046.5625MB
% 0.09/0.35  % OS       : Linux 6.8.0-71-generic
% 0.09/0.35  % CPULimit : 300
% 0.09/0.35  % WCLimit  : 300
% 0.09/0.35  % DateTime : Sun Sep 27 09:14:06 UTC 2026
% 0.09/0.35  % CPUTime  : 
% 0.09/0.35  Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 144.57/18.64  Command-line arguments: --no-flatten-goal
% 144.57/18.64  
% 144.57/18.64  % SZS status Unsatisfiable
% 144.57/18.64  
% 144.57/18.69  % SZS output start CNFRefutation
% See solution above
% 147.95/19.07  
% 147.95/19.07  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------