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Twee---2.7.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : BOO076-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n011.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 09:35:44 AM UTC 2026

% Result   : Unsatisfiable 76.27s 9.97s
% Output   : CNFRefutation 93.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :  182
%            Number of leaves      :    2
% Syntax   : Number of clauses     : 1300 (1300 unt;   0 nHn;   4 RR)
%            Number of literals    : 1300 (1299 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   13 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   : 3786 ( 313 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
    nand(a,nand(b,nand(a,c))) != nand(nand(nand(c,b),b),a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_meredith_2_basis_2) ).

cnf(c2,axiom,
    nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,A))) = B,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sh_1) ).

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

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

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

cnf(c6,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X3,X2)),nand(X3,X2))),nand(nand(X2,nand(nand(X,X2),X2)),nand(X,nand(X3,X2)))) = nand(X2,nand(nand(X,X2),X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c7,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X3,X2)),nand(X3,X2))),X) = nand(X2,nand(nand(X,X2),X2)),
    inference(transitivity,[status(thm)],[c5,c6]) ).

cnf(c8,plain,
    nand(nand(nand(X2,X2),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X2,X2)),nand(X2,X2))),X) = nand(X2,nand(nand(X,X2),X2)),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c9,plain,
    nand(X2,nand(nand(X,X2),X2)) = nand(nand(nand(X2,X2),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X2,X2)),nand(X2,X2))),X),
    inference(symmetry,[status(thm)],[c8]) ).

cnf(c10,plain,
    nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(X,X2))) = X2,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c11,plain,
    X2 = nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(X,X2))),
    inference(symmetry,[status(thm)],[c10]) ).

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

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

cnf(c14,plain,
    nand(nand(nand(X2,nand(X,X2)),nand(X2,nand(X2,nand(X,X2)))),X2) = nand(nand(nand(X2,nand(X,X2)),nand(nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(X,X2))),nand(X2,nand(X,X2)))),X2),
    inference(congruence,[status(thm)],[c13]) ).

cnf(c15,plain,
    nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X2,X),X))) = X,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c16,plain,
    X = nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X2,X),X))),
    inference(symmetry,[status(thm)],[c15]) ).

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

cnf(c18,plain,
    nand(nand(X,nand(nand(X2,X),X)),nand(X2,nand(X3,X))) = X2,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c19,plain,
    X3 = nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))),
    inference(symmetry,[status(thm)],[c18]) ).

cnf(c20,plain,
    nand(X3,X4) = nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),
    inference(congruence,[status(thm)],[c19]) ).

cnf(c21,plain,
    nand(nand(X3,X4),X4) = nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4),
    inference(congruence,[status(thm)],[c20]) ).

cnf(c22,plain,
    nand(X4,nand(nand(X3,X4),X4)) = nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4)),
    inference(congruence,[status(thm)],[c21]) ).

cnf(c23,plain,
    nand(nand(X4,nand(nand(X3,X4),X4)),nand(X3,nand(X2,nand(nand(X4,X2),X2)))) = nand(nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4)),nand(X3,nand(X2,nand(nand(X4,X2),X2)))),
    inference(congruence,[status(thm)],[c22]) ).

cnf(c24,plain,
    nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))) = X3,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c25,plain,
    X3 = nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))),
    inference(symmetry,[status(thm)],[c24]) ).

cnf(c26,plain,
    nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4) = nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),
    inference(congruence,[status(thm)],[c25]) ).

cnf(c27,plain,
    nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4)) = nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),
    inference(congruence,[status(thm)],[c26]) ).

cnf(c28,plain,
    nand(nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4)),nand(X3,nand(X2,nand(nand(X4,X2),X2)))) = nand(nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X3,nand(X2,nand(nand(X4,X2),X2)))),
    inference(congruence,[status(thm)],[c27]) ).

cnf(c29,plain,
    nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))) = X3,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c30,plain,
    X3 = nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))),
    inference(symmetry,[status(thm)],[c29]) ).

cnf(c31,plain,
    nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))) = nand(nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))),nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),
    inference(congruence,[status(thm)],[c30]) ).

cnf(c32,plain,
    nand(nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X3,nand(X2,nand(nand(X4,X2),X2)))) = nand(nand(nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))),nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X3,nand(X2,nand(nand(X4,X2),X2)))),
    inference(congruence,[status(thm)],[c31]) ).

cnf(c33,plain,
    nand(nand(X,nand(nand(X3,X),X)),nand(X3,nand(X2,X))) = X3,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c34,plain,
    X3 = nand(nand(X,nand(nand(X3,X),X)),nand(X3,nand(X2,X))),
    inference(symmetry,[status(thm)],[c33]) ).

cnf(c35,plain,
    nand(X,X4) = nand(X,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X3,X2)))),
    inference(congruence,[status(thm)],[c34]) ).

cnf(c36,plain,
    nand(nand(nand(X4,nand(X3,X2)),nand(nand(X,nand(X4,nand(X3,X2))),nand(X4,nand(X3,X2)))),nand(X,X4)) = nand(nand(nand(X4,nand(X3,X2)),nand(nand(X,nand(X4,nand(X3,X2))),nand(X4,nand(X3,X2)))),nand(X,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X3,X2))))),
    inference(congruence,[status(thm)],[c35]) ).

cnf(c37,plain,
    nand(nand(nand(X4,nand(X3,X2)),nand(nand(X,nand(X4,nand(X3,X2))),nand(X4,nand(X3,X2)))),nand(X,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X3,X2))))) = X,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c38,plain,
    nand(nand(nand(X4,nand(X3,X2)),nand(nand(X,nand(X4,nand(X3,X2))),nand(X4,nand(X3,X2)))),nand(X,X4)) = X,
    inference(transitivity,[status(thm)],[c36,c37]) ).

cnf(c39,plain,
    nand(nand(nand(X2,nand(X,X4)),nand(nand(X3,nand(X2,nand(X,X4))),nand(X2,nand(X,X4)))),nand(X3,X2)) = X3,
    inference(substitution,[status(thm)],[c38]) ).

cnf(c40,plain,
    X4 = nand(nand(nand(X3,nand(X2,X)),nand(nand(X4,nand(X3,nand(X2,X))),nand(X3,nand(X2,X)))),nand(X4,X3)),
    inference(symmetry,[status(thm)],[c39]) ).

cnf(c41,plain,
    nand(X3,X5) = nand(X3,nand(nand(nand(X4,nand(X2,X)),nand(nand(X5,nand(X4,nand(X2,X))),nand(X4,nand(X2,X)))),nand(X5,X4))),
    inference(congruence,[status(thm)],[c40]) ).

cnf(c42,plain,
    nand(nand(nand(X5,X4),nand(nand(X3,nand(X5,X4)),nand(X5,X4))),nand(X3,X5)) = nand(nand(nand(X5,X4),nand(nand(X3,nand(X5,X4)),nand(X5,X4))),nand(X3,nand(nand(nand(X4,nand(X2,X)),nand(nand(X5,nand(X4,nand(X2,X))),nand(X4,nand(X2,X)))),nand(X5,X4)))),
    inference(congruence,[status(thm)],[c41]) ).

cnf(c43,plain,
    nand(nand(nand(X5,X4),nand(nand(X3,nand(X5,X4)),nand(X5,X4))),nand(X3,nand(nand(nand(X4,nand(X2,X)),nand(nand(X5,nand(X4,nand(X2,X))),nand(X4,nand(X2,X)))),nand(X5,X4)))) = X3,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c44,plain,
    nand(nand(nand(X3,X2),nand(nand(X,nand(X3,X2)),nand(X3,X2))),nand(X,X3)) = X,
    inference(transitivity,[status(thm)],[c42,c43]) ).

cnf(c45,plain,
    nand(nand(nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))),nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X3,nand(X2,nand(nand(X4,X2),X2)))) = X3,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c46,plain,
    nand(nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X3,nand(X2,nand(nand(X4,X2),X2)))) = X3,
    inference(transitivity,[status(thm)],[c32,c45]) ).

cnf(c47,plain,
    nand(nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4)),nand(X3,nand(X2,nand(nand(X4,X2),X2)))) = X3,
    inference(transitivity,[status(thm)],[c28,c46]) ).

cnf(c48,plain,
    nand(nand(X3,nand(nand(X2,X3),X3)),nand(X2,nand(X,nand(nand(X3,X),X)))) = X2,
    inference(transitivity,[status(thm)],[c23,c47]) ).

cnf(c49,plain,
    nand(nand(X2,nand(nand(nand(X,nand(nand(X,X),X)),X2),X2)),nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X2,X),X)))) = nand(X,nand(nand(X,X),X)),
    inference(substitution,[status(thm)],[c48]) ).

cnf(c50,plain,
    nand(nand(X2,nand(nand(nand(X,nand(nand(X,X),X)),X2),X2)),X) = nand(X,nand(nand(X,X),X)),
    inference(transitivity,[status(thm)],[c17,c49]) ).

cnf(c51,plain,
    nand(nand(nand(X2,nand(X,X2)),nand(nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(X,X2))),nand(X2,nand(X,X2)))),X2) = nand(X2,nand(nand(X2,X2),X2)),
    inference(substitution,[status(thm)],[c50]) ).

cnf(c52,plain,
    nand(nand(nand(X2,nand(X,X2)),nand(X2,nand(X2,nand(X,X2)))),X2) = nand(X2,nand(nand(X2,X2),X2)),
    inference(transitivity,[status(thm)],[c14,c51]) ).

cnf(c53,plain,
    nand(nand(nand(X,nand(nand(X,X),X)),nand(X,nand(X,nand(nand(X,X),X)))),X) = nand(X,nand(nand(X,X),X)),
    inference(substitution,[status(thm)],[c52]) ).

cnf(c54,plain,
    nand(X,nand(nand(X,X),X)) = nand(nand(nand(X,nand(nand(X,X),X)),nand(X,nand(X,nand(nand(X,X),X)))),X),
    inference(symmetry,[status(thm)],[c53]) ).

cnf(c55,plain,
    nand(nand(X,nand(nand(X,X),X)),nand(X,nand(X,nand(nand(X,X),X)))) = X,
    inference(substitution,[status(thm)],[c48]) ).

cnf(c56,plain,
    nand(nand(nand(X,nand(nand(X,X),X)),nand(X,nand(X,nand(nand(X,X),X)))),X) = nand(X,X),
    inference(congruence,[status(thm)],[c55]) ).

cnf(c57,plain,
    nand(X,nand(nand(X,X),X)) = nand(X,X),
    inference(transitivity,[status(thm)],[c54,c56]) ).

cnf(c58,plain,
    nand(X,X) = nand(X,nand(nand(X,X),X)),
    inference(symmetry,[status(thm)],[c57]) ).

cnf(c59,plain,
    nand(nand(X,X),nand(X,X)) = nand(nand(X,nand(nand(X,X),X)),nand(X,X)),
    inference(congruence,[status(thm)],[c58]) ).

cnf(c60,plain,
    nand(X,X) = nand(X,nand(nand(X,X),X)),
    inference(symmetry,[status(thm)],[c57]) ).

cnf(c61,plain,
    nand(nand(X,nand(nand(X,X),X)),nand(X,X)) = nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),
    inference(congruence,[status(thm)],[c60]) ).

cnf(c62,plain,
    nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))) = X,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c63,plain,
    nand(nand(X,nand(nand(X,X),X)),nand(X,X)) = X,
    inference(transitivity,[status(thm)],[c61,c62]) ).

cnf(c64,plain,
    nand(nand(X,X),nand(X,X)) = X,
    inference(transitivity,[status(thm)],[c59,c63]) ).

cnf(c65,plain,
    X = nand(nand(X,X),nand(X,X)),
    inference(symmetry,[status(thm)],[c64]) ).

cnf(c66,plain,
    nand(X2,nand(nand(X2,X),nand(X2,nand(X2,X)))) = nand(nand(nand(X2,X2),nand(X2,X2)),nand(nand(X2,X),nand(X2,nand(X2,X)))),
    inference(congruence,[status(thm)],[c65]) ).

cnf(c67,plain,
    X = nand(nand(X,X),nand(X,X)),
    inference(symmetry,[status(thm)],[c64]) ).

cnf(c68,plain,
    nand(X,nand(X,X)) = nand(nand(nand(X,X),nand(X,X)),nand(X,X)),
    inference(congruence,[status(thm)],[c67]) ).

cnf(c69,plain,
    nand(nand(X,X),nand(X,nand(X,X))) = nand(nand(X,X),nand(nand(nand(X,X),nand(X,X)),nand(X,X))),
    inference(congruence,[status(thm)],[c68]) ).

cnf(c70,plain,
    nand(nand(X,X),nand(nand(nand(X,X),nand(X,X)),nand(X,X))) = nand(nand(X,X),nand(X,X)),
    inference(substitution,[status(thm)],[c57]) ).

cnf(c71,plain,
    nand(nand(X,X),nand(nand(nand(X,X),nand(X,X)),nand(X,X))) = X,
    inference(transitivity,[status(thm)],[c70,c64]) ).

cnf(c72,plain,
    nand(nand(X,X),nand(X,nand(X,X))) = X,
    inference(transitivity,[status(thm)],[c69,c71]) ).

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

cnf(c74,plain,
    nand(X,nand(X2,nand(nand(X,X2),X2))) = nand(nand(nand(X,X),nand(X,nand(X,X))),nand(X2,nand(nand(X,X2),X2))),
    inference(congruence,[status(thm)],[c73]) ).

cnf(c75,plain,
    nand(nand(X2,nand(nand(X,X2),X2)),nand(X,nand(X2,nand(nand(X,X2),X2)))) = nand(nand(X2,nand(nand(X,X2),X2)),nand(nand(nand(X,X),nand(X,nand(X,X))),nand(X2,nand(nand(X,X2),X2)))),
    inference(congruence,[status(thm)],[c74]) ).

cnf(c76,plain,
    nand(X,X) = nand(X,nand(nand(X,X),X)),
    inference(symmetry,[status(thm)],[c57]) ).

cnf(c77,plain,
    nand(nand(X2,nand(nand(X,X2),X2)),nand(X,X)) = nand(nand(X2,nand(nand(X,X2),X2)),nand(X,nand(nand(X,X),X))),
    inference(congruence,[status(thm)],[c76]) ).

cnf(c78,plain,
    nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))) = X,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c79,plain,
    X = nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),
    inference(symmetry,[status(thm)],[c78]) ).

cnf(c80,plain,
    nand(X,X2) = nand(nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),X2),
    inference(congruence,[status(thm)],[c79]) ).

cnf(c81,plain,
    nand(nand(X,X2),X2) = nand(nand(nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),X2),X2),
    inference(congruence,[status(thm)],[c80]) ).

cnf(c82,plain,
    nand(X2,nand(nand(X,X2),X2)) = nand(X2,nand(nand(nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),X2),X2)),
    inference(congruence,[status(thm)],[c81]) ).

cnf(c83,plain,
    nand(nand(X2,nand(nand(X,X2),X2)),nand(X,nand(nand(X,X),X))) = nand(nand(X2,nand(nand(nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),X2),X2)),nand(X,nand(nand(X,X),X))),
    inference(congruence,[status(thm)],[c82]) ).

cnf(c84,plain,
    nand(X,X) = nand(X,nand(nand(X,X),X)),
    inference(symmetry,[status(thm)],[c57]) ).

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

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

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

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

cnf(c89,plain,
    nand(nand(X2,nand(nand(nand(X,nand(nand(X,X),X)),X2),X2)),X) = nand(X,X),
    inference(transitivity,[status(thm)],[c50,c57]) ).

cnf(c90,plain,
    nand(nand(X2,nand(nand(nand(X,X),X2),X2)),X) = nand(X,X),
    inference(transitivity,[status(thm)],[c88,c89]) ).

cnf(c91,plain,
    nand(nand(X2,nand(nand(nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),X2),X2)),nand(X,nand(nand(X,X),X))) = nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),
    inference(substitution,[status(thm)],[c90]) ).

cnf(c92,plain,
    nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))) = X,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c93,plain,
    nand(nand(X2,nand(nand(nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),X2),X2)),nand(X,nand(nand(X,X),X))) = X,
    inference(transitivity,[status(thm)],[c91,c92]) ).

cnf(c94,plain,
    nand(nand(X2,nand(nand(X,X2),X2)),nand(X,nand(nand(X,X),X))) = X,
    inference(transitivity,[status(thm)],[c83,c93]) ).

cnf(c95,plain,
    nand(nand(X2,nand(nand(X,X2),X2)),nand(X,X)) = X,
    inference(transitivity,[status(thm)],[c77,c94]) ).

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

cnf(c97,plain,
    nand(X,nand(X,X)) = nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X,X)),nand(X,X)),
    inference(congruence,[status(thm)],[c96]) ).

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

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

cnf(c100,plain,
    nand(nand(X2,nand(nand(X,X2),X2)),nand(nand(nand(X,X),nand(X,nand(X,X))),nand(X2,nand(nand(X,X2),X2)))) = nand(nand(X2,nand(nand(X,X2),X2)),nand(nand(nand(X,X),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X,X)),nand(X,X))),nand(X2,nand(nand(X,X2),X2)))),
    inference(congruence,[status(thm)],[c99]) ).

cnf(c101,plain,
    X = nand(nand(X,X),nand(X,nand(X,X))),
    inference(symmetry,[status(thm)],[c72]) ).

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

cnf(c103,plain,
    nand(nand(X,nand(nand(X2,X),X)),nand(X2,X2)) = X2,
    inference(substitution,[status(thm)],[c95]) ).

cnf(c104,plain,
    X2 = nand(nand(X,nand(nand(X2,X),X)),nand(X2,X2)),
    inference(symmetry,[status(thm)],[c103]) ).

cnf(c105,plain,
    nand(X2,nand(X2,X2)) = nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X2)),nand(X2,X2)),
    inference(congruence,[status(thm)],[c104]) ).

cnf(c106,plain,
    nand(nand(X2,X2),nand(X2,nand(X2,X2))) = nand(nand(X2,X2),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X2)),nand(X2,X2))),
    inference(congruence,[status(thm)],[c105]) ).

cnf(c107,plain,
    nand(nand(nand(X2,X2),nand(X2,nand(X2,X2))),nand(nand(X,nand(nand(X2,X),X)),X2)) = nand(nand(nand(X2,X2),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X2)),nand(X2,X2))),nand(nand(X,nand(nand(X2,X),X)),X2)),
    inference(congruence,[status(thm)],[c106]) ).

cnf(c108,plain,
    nand(nand(nand(X2,X2),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X2)),nand(X2,X2))),nand(nand(X,nand(nand(X2,X),X)),X2)) = nand(X,nand(nand(X2,X),X)),
    inference(substitution,[status(thm)],[c44]) ).

cnf(c109,plain,
    nand(nand(nand(X2,X2),nand(X2,nand(X2,X2))),nand(nand(X,nand(nand(X2,X),X)),X2)) = nand(X,nand(nand(X2,X),X)),
    inference(transitivity,[status(thm)],[c107,c108]) ).

cnf(c110,plain,
    nand(X2,nand(nand(X,nand(nand(X2,X),X)),X2)) = nand(X,nand(nand(X2,X),X)),
    inference(transitivity,[status(thm)],[c102,c109]) ).

cnf(c111,plain,
    nand(nand(X2,nand(nand(X,X2),X2)),nand(nand(nand(X,X),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X,X)),nand(X,X))),nand(X2,nand(nand(X,X2),X2)))) = nand(nand(X,X),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X,X)),nand(X,X))),
    inference(substitution,[status(thm)],[c110]) ).

cnf(c112,plain,
    nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X,X)),nand(X,X)) = nand(X,nand(X,X)),
    inference(congruence,[status(thm)],[c95]) ).

cnf(c113,plain,
    nand(nand(X,X),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X,X)),nand(X,X))) = nand(nand(X,X),nand(X,nand(X,X))),
    inference(congruence,[status(thm)],[c112]) ).

cnf(c114,plain,
    nand(nand(X,X),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X,X)),nand(X,X))) = X,
    inference(transitivity,[status(thm)],[c113,c72]) ).

cnf(c115,plain,
    nand(nand(X2,nand(nand(X,X2),X2)),nand(nand(nand(X,X),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X,X)),nand(X,X))),nand(X2,nand(nand(X,X2),X2)))) = X,
    inference(transitivity,[status(thm)],[c111,c114]) ).

cnf(c116,plain,
    nand(nand(X2,nand(nand(X,X2),X2)),nand(nand(nand(X,X),nand(X,nand(X,X))),nand(X2,nand(nand(X,X2),X2)))) = X,
    inference(transitivity,[status(thm)],[c100,c115]) ).

cnf(c117,plain,
    nand(nand(X2,nand(nand(X,X2),X2)),nand(X,nand(X2,nand(nand(X,X2),X2)))) = X,
    inference(transitivity,[status(thm)],[c75,c116]) ).

cnf(c118,plain,
    nand(nand(X,nand(nand(nand(X2,X2),X),X)),nand(nand(X2,X2),nand(X,nand(nand(nand(X2,X2),X),X)))) = nand(X2,X2),
    inference(substitution,[status(thm)],[c117]) ).

cnf(c119,plain,
    nand(X2,X2) = nand(nand(X,nand(nand(nand(X2,X2),X),X)),nand(nand(X2,X2),nand(X,nand(nand(nand(X2,X2),X),X)))),
    inference(symmetry,[status(thm)],[c118]) ).

cnf(c120,plain,
    nand(nand(X2,X2),nand(X2,X)) = nand(nand(nand(X,nand(nand(nand(X2,X2),X),X)),nand(nand(X2,X2),nand(X,nand(nand(nand(X2,X2),X),X)))),nand(X2,X)),
    inference(congruence,[status(thm)],[c119]) ).

cnf(c121,plain,
    nand(nand(X2,X2),nand(nand(X,nand(nand(nand(X2,X2),X),X)),nand(X2,X2))) = nand(X,nand(nand(nand(X2,X2),X),X)),
    inference(substitution,[status(thm)],[c110]) ).

cnf(c122,plain,
    nand(X,nand(nand(nand(X2,X2),X),X)) = nand(nand(X2,X2),nand(nand(X,nand(nand(nand(X2,X2),X),X)),nand(X2,X2))),
    inference(symmetry,[status(thm)],[c121]) ).

cnf(c123,plain,
    nand(X2,nand(X,nand(nand(nand(X2,X2),X),X))) = nand(X2,nand(nand(X2,X2),nand(nand(X,nand(nand(nand(X2,X2),X),X)),nand(X2,X2)))),
    inference(congruence,[status(thm)],[c122]) ).

cnf(c124,plain,
    nand(X,X) = nand(X,nand(nand(X,X),X)),
    inference(symmetry,[status(thm)],[c57]) ).

cnf(c125,plain,
    nand(nand(X2,X2),nand(X,nand(X2,X2))) = nand(nand(X2,nand(nand(X2,X2),X2)),nand(X,nand(X2,X2))),
    inference(congruence,[status(thm)],[c124]) ).

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

cnf(c127,plain,
    nand(X,X) = nand(X,nand(nand(X,X),X)),
    inference(symmetry,[status(thm)],[c57]) ).

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

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

cnf(c130,plain,
    nand(X2,nand(nand(X2,nand(nand(X2,X2),X2)),nand(X,nand(X2,X2)))) = nand(X2,nand(nand(X2,nand(nand(X2,X2),X2)),nand(X,nand(X2,nand(nand(X2,X2),X2))))),
    inference(congruence,[status(thm)],[c129]) ).

cnf(c131,plain,
    nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))) = X,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c132,plain,
    X = nand(nand(X,nand(nand(X,X),X)),nand(X,nand(nand(X,X),X))),
    inference(symmetry,[status(thm)],[c131]) ).

cnf(c133,plain,
    nand(X2,nand(nand(X2,nand(nand(X2,X2),X2)),nand(X,nand(X2,nand(nand(X2,X2),X2))))) = nand(nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(nand(X2,X2),X2))),nand(nand(X2,nand(nand(X2,X2),X2)),nand(X,nand(X2,nand(nand(X2,X2),X2))))),
    inference(congruence,[status(thm)],[c132]) ).

cnf(c134,plain,
    nand(X,X) = nand(X,nand(nand(X,X),X)),
    inference(symmetry,[status(thm)],[c57]) ).

cnf(c135,plain,
    nand(nand(X2,X2),nand(X2,nand(X,X2))) = nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(X,X2))),
    inference(congruence,[status(thm)],[c134]) ).

cnf(c136,plain,
    nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(X,X2))) = X2,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c137,plain,
    nand(nand(X2,X2),nand(X2,nand(X,X2))) = X2,
    inference(transitivity,[status(thm)],[c135,c136]) ).

cnf(c138,plain,
    nand(nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(nand(X2,X2),X2))),nand(nand(X2,nand(nand(X2,X2),X2)),nand(X,nand(X2,nand(nand(X2,X2),X2))))) = nand(X2,nand(nand(X2,X2),X2)),
    inference(substitution,[status(thm)],[c137]) ).

cnf(c139,plain,
    nand(nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(nand(X2,X2),X2))),nand(nand(X2,nand(nand(X2,X2),X2)),nand(X,nand(X2,nand(nand(X2,X2),X2))))) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c138,c57]) ).

cnf(c140,plain,
    nand(X2,nand(nand(X2,nand(nand(X2,X2),X2)),nand(X,nand(X2,nand(nand(X2,X2),X2))))) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c133,c139]) ).

cnf(c141,plain,
    nand(X2,nand(nand(X2,nand(nand(X2,X2),X2)),nand(X,nand(X2,X2)))) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c130,c140]) ).

cnf(c142,plain,
    nand(X2,nand(nand(X2,X2),nand(X,nand(X2,X2)))) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c126,c141]) ).

cnf(c143,plain,
    nand(X2,nand(nand(X2,X2),nand(nand(X,nand(nand(nand(X2,X2),X),X)),nand(X2,X2)))) = nand(X2,X2),
    inference(substitution,[status(thm)],[c142]) ).

cnf(c144,plain,
    nand(X2,nand(X,nand(nand(nand(X2,X2),X),X))) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c123,c143]) ).

cnf(c145,plain,
    nand(X2,X2) = nand(X2,nand(X,nand(nand(nand(X2,X2),X),X))),
    inference(symmetry,[status(thm)],[c144]) ).

cnf(c146,plain,
    nand(nand(X2,X2),nand(X,nand(nand(nand(X2,X2),X),X))) = nand(nand(X2,nand(X,nand(nand(nand(X2,X2),X),X))),nand(X,nand(nand(nand(X2,X2),X),X))),
    inference(congruence,[status(thm)],[c145]) ).

cnf(c147,plain,
    nand(nand(X,nand(nand(nand(X2,X2),X),X)),nand(nand(X2,X2),nand(X,nand(nand(nand(X2,X2),X),X)))) = nand(nand(X,nand(nand(nand(X2,X2),X),X)),nand(nand(X2,nand(X,nand(nand(nand(X2,X2),X),X))),nand(X,nand(nand(nand(X2,X2),X),X)))),
    inference(congruence,[status(thm)],[c146]) ).

cnf(c148,plain,
    nand(nand(nand(X,nand(nand(nand(X2,X2),X),X)),nand(nand(X2,X2),nand(X,nand(nand(nand(X2,X2),X),X)))),nand(X2,X)) = nand(nand(nand(X,nand(nand(nand(X2,X2),X),X)),nand(nand(X2,nand(X,nand(nand(nand(X2,X2),X),X))),nand(X,nand(nand(nand(X2,X2),X),X)))),nand(X2,X)),
    inference(congruence,[status(thm)],[c147]) ).

cnf(c149,plain,
    nand(nand(nand(X,nand(nand(nand(X2,X2),X),X)),nand(nand(X2,nand(X,nand(nand(nand(X2,X2),X),X))),nand(X,nand(nand(nand(X2,X2),X),X)))),nand(X2,X)) = X2,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c150,plain,
    nand(nand(nand(X,nand(nand(nand(X2,X2),X),X)),nand(nand(X2,X2),nand(X,nand(nand(nand(X2,X2),X),X)))),nand(X2,X)) = X2,
    inference(transitivity,[status(thm)],[c148,c149]) ).

cnf(c151,plain,
    nand(nand(X2,X2),nand(X2,X)) = X2,
    inference(transitivity,[status(thm)],[c120,c150]) ).

cnf(c152,plain,
    X2 = nand(nand(X2,X2),nand(X2,X)),
    inference(symmetry,[status(thm)],[c151]) ).

cnf(c153,plain,
    nand(X2,nand(X2,X)) = nand(nand(nand(X2,X2),nand(X2,X)),nand(X2,X)),
    inference(congruence,[status(thm)],[c152]) ).

cnf(c154,plain,
    nand(nand(X2,X),nand(X2,nand(X2,X))) = nand(nand(X2,X),nand(nand(nand(X2,X2),nand(X2,X)),nand(X2,X))),
    inference(congruence,[status(thm)],[c153]) ).

cnf(c155,plain,
    nand(nand(nand(X2,X2),nand(X2,X2)),nand(nand(X2,X),nand(X2,nand(X2,X)))) = nand(nand(nand(X2,X2),nand(X2,X2)),nand(nand(X2,X),nand(nand(nand(X2,X2),nand(X2,X)),nand(X2,X)))),
    inference(congruence,[status(thm)],[c154]) ).

cnf(c156,plain,
    nand(X,X) = nand(X,nand(nand(X,X),X)),
    inference(symmetry,[status(thm)],[c57]) ).

cnf(c157,plain,
    nand(nand(X2,X2),nand(X,nand(nand(X2,X),X))) = nand(nand(X2,nand(nand(X2,X2),X2)),nand(X,nand(nand(X2,X),X))),
    inference(congruence,[status(thm)],[c156]) ).

cnf(c158,plain,
    nand(X,nand(nand(X2,X),X)) = nand(X2,nand(nand(X,nand(nand(X2,X),X)),X2)),
    inference(symmetry,[status(thm)],[c110]) ).

cnf(c159,plain,
    nand(nand(X2,nand(nand(X2,X2),X2)),nand(X,nand(nand(X2,X),X))) = nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(nand(X,nand(nand(X2,X),X)),X2))),
    inference(congruence,[status(thm)],[c158]) ).

cnf(c160,plain,
    nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(nand(X,nand(nand(X2,X),X)),X2))) = X2,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c161,plain,
    nand(nand(X2,nand(nand(X2,X2),X2)),nand(X,nand(nand(X2,X),X))) = X2,
    inference(transitivity,[status(thm)],[c159,c160]) ).

cnf(c162,plain,
    nand(nand(X2,X2),nand(X,nand(nand(X2,X),X))) = X2,
    inference(transitivity,[status(thm)],[c157,c161]) ).

cnf(c163,plain,
    nand(nand(nand(X2,X2),nand(X2,X2)),nand(nand(X2,X),nand(nand(nand(X2,X2),nand(X2,X)),nand(X2,X)))) = nand(X2,X2),
    inference(substitution,[status(thm)],[c162]) ).

cnf(c164,plain,
    nand(nand(nand(X2,X2),nand(X2,X2)),nand(nand(X2,X),nand(X2,nand(X2,X)))) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c155,c163]) ).

cnf(c165,plain,
    nand(X2,nand(nand(X2,X),nand(X2,nand(X2,X)))) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c66,c164]) ).

cnf(c166,plain,
    nand(X2,nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X))))) = nand(X2,X2),
    inference(substitution,[status(thm)],[c165]) ).

cnf(c167,plain,
    nand(X2,X2) = nand(X2,nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X))))),
    inference(symmetry,[status(thm)],[c166]) ).

cnf(c168,plain,
    nand(nand(X2,X),nand(X2,X2)) = nand(nand(X2,X),nand(X2,nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X)))))),
    inference(congruence,[status(thm)],[c167]) ).

cnf(c169,plain,
    X2 = nand(nand(X2,X2),nand(X2,X)),
    inference(symmetry,[status(thm)],[c151]) ).

cnf(c170,plain,
    nand(X2,nand(X2,X)) = nand(nand(nand(X2,X2),nand(X2,X)),nand(X2,X)),
    inference(congruence,[status(thm)],[c169]) ).

cnf(c171,plain,
    nand(nand(X2,X),nand(X2,nand(X2,X))) = nand(nand(X2,X),nand(nand(nand(X2,X2),nand(X2,X)),nand(X2,X))),
    inference(congruence,[status(thm)],[c170]) ).

cnf(c172,plain,
    nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2)) = X3,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c173,plain,
    X3 = nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2)),
    inference(symmetry,[status(thm)],[c172]) ).

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

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

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

cnf(c177,plain,
    nand(nand(X3,X2),nand(nand(nand(X3,X3),nand(X3,X2)),nand(X3,X2))) = nand(nand(X3,X2),nand(nand(nand(X3,nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),
    inference(congruence,[status(thm)],[c176]) ).

cnf(c178,plain,
    nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2)) = X3,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c179,plain,
    X3 = nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2)),
    inference(symmetry,[status(thm)],[c178]) ).

cnf(c180,plain,
    nand(X3,nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2))) = nand(nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2)),nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2))),
    inference(congruence,[status(thm)],[c179]) ).

cnf(c181,plain,
    nand(nand(X3,nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2))),nand(X3,X2)) = nand(nand(nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2)),nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2))),nand(X3,X2)),
    inference(congruence,[status(thm)],[c180]) ).

cnf(c182,plain,
    nand(nand(nand(X3,nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2))),nand(X3,X2)),nand(X3,X2)) = nand(nand(nand(nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2)),nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2))),nand(X3,X2)),nand(X3,X2)),
    inference(congruence,[status(thm)],[c181]) ).

cnf(c183,plain,
    nand(nand(X3,X2),nand(nand(nand(X3,nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2))),nand(X3,X2)),nand(X3,X2))) = nand(nand(X3,X2),nand(nand(nand(nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2)),nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),
    inference(congruence,[status(thm)],[c182]) ).

cnf(c184,plain,
    nand(nand(nand(X,X2),nand(nand(nand(X2,nand(nand(nand(nand(X,X2),nand(X,X2)),X2),X2)),nand(X,X2)),nand(X,X2))),nand(nand(X,X2),nand(X,X2))) = nand(X2,nand(nand(nand(nand(X,X2),nand(X,X2)),X2),X2)),
    inference(substitution,[status(thm)],[c7]) ).

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

cnf(c186,plain,
    nand(nand(X2,nand(nand(nand(nand(X,X2),nand(X,X2)),X2),X2)),nand(X,X2)) = nand(nand(X,X2),nand(X,X2)),
    inference(substitution,[status(thm)],[c90]) ).

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

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

cnf(c189,plain,
    nand(nand(nand(X,X2),nand(nand(nand(X2,nand(nand(nand(nand(X,X2),nand(X,X2)),X2),X2)),nand(X,X2)),nand(X,X2))),nand(nand(X,X2),nand(X,X2))) = nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),nand(nand(X,X2),nand(X,X2))),
    inference(congruence,[status(thm)],[c188]) ).

cnf(c190,plain,
    nand(nand(nand(X,X2),nand(nand(nand(X,X2),nand(X,X2)),nand(X,X2))),nand(nand(X,X2),nand(X,X2))) = nand(X,X2),
    inference(substitution,[status(thm)],[c95]) ).

cnf(c191,plain,
    nand(nand(nand(X,X2),nand(nand(nand(X2,nand(nand(nand(nand(X,X2),nand(X,X2)),X2),X2)),nand(X,X2)),nand(X,X2))),nand(nand(X,X2),nand(X,X2))) = nand(X,X2),
    inference(transitivity,[status(thm)],[c189,c190]) ).

cnf(c192,plain,
    nand(X2,nand(nand(nand(nand(X,X2),nand(X,X2)),X2),X2)) = nand(X,X2),
    inference(transitivity,[status(thm)],[c185,c191]) ).

cnf(c193,plain,
    nand(nand(X3,X2),nand(nand(nand(nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2)),nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2))),nand(X3,X2)),nand(X3,X2))) = nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2)),
    inference(substitution,[status(thm)],[c192]) ).

cnf(c194,plain,
    nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2)) = X3,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c195,plain,
    nand(nand(X3,X2),nand(nand(nand(nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2)),nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2))),nand(X3,X2)),nand(X3,X2))) = X3,
    inference(transitivity,[status(thm)],[c193,c194]) ).

cnf(c196,plain,
    nand(nand(X3,X2),nand(nand(nand(X3,nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2))),nand(X3,X2)),nand(X3,X2))) = X3,
    inference(transitivity,[status(thm)],[c183,c195]) ).

cnf(c197,plain,
    nand(nand(X2,X),nand(nand(nand(X2,X2),nand(X2,X)),nand(X2,X))) = X2,
    inference(transitivity,[status(thm)],[c177,c196]) ).

cnf(c198,plain,
    nand(nand(X2,X),nand(X2,nand(X2,X))) = X2,
    inference(transitivity,[status(thm)],[c171,c197]) ).

cnf(c199,plain,
    X2 = nand(nand(X2,X),nand(X2,nand(X2,X))),
    inference(symmetry,[status(thm)],[c198]) ).

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

cnf(c201,plain,
    nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X)))) = nand(nand(X2,nand(X2,X)),nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X)))),
    inference(congruence,[status(thm)],[c200]) ).

cnf(c202,plain,
    nand(X2,nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X))))) = nand(X2,nand(nand(X2,nand(X2,X)),nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X))))),
    inference(congruence,[status(thm)],[c201]) ).

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

cnf(c204,plain,
    nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X)))) = X2,
    inference(substitution,[status(thm)],[c198]) ).

cnf(c205,plain,
    X2 = nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X)))),
    inference(symmetry,[status(thm)],[c204]) ).

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

cnf(c207,plain,
    nand(nand(X2,X),nand(X2,nand(nand(X2,nand(X2,X)),nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X)))))) = nand(nand(X2,X),nand(nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X)))),nand(nand(X2,nand(X2,X)),nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X)))))),
    inference(congruence,[status(thm)],[c206]) ).

cnf(c208,plain,
    X2 = nand(nand(X2,X),nand(X2,nand(X2,X))),
    inference(symmetry,[status(thm)],[c198]) ).

cnf(c209,plain,
    nand(X2,nand(X2,nand(X2,X))) = nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X))),
    inference(congruence,[status(thm)],[c208]) ).

cnf(c210,plain,
    nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X)))) = nand(nand(X2,nand(X2,X)),nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X)))),
    inference(congruence,[status(thm)],[c209]) ).

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

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

cnf(c213,plain,
    X = nand(nand(X,X),nand(X,nand(X,X))),
    inference(symmetry,[status(thm)],[c72]) ).

cnf(c214,plain,
    nand(X2,nand(nand(X,nand(nand(X2,X),X)),nand(X,nand(nand(X2,X),X)))) = nand(nand(nand(X2,X2),nand(X2,nand(X2,X2))),nand(nand(X,nand(nand(X2,X),X)),nand(X,nand(nand(X2,X),X)))),
    inference(congruence,[status(thm)],[c213]) ).

cnf(c215,plain,
    nand(nand(X,nand(nand(X2,X),X)),nand(X2,X2)) = X2,
    inference(substitution,[status(thm)],[c95]) ).

cnf(c216,plain,
    X2 = nand(nand(X,nand(nand(X2,X),X)),nand(X2,X2)),
    inference(symmetry,[status(thm)],[c215]) ).

cnf(c217,plain,
    nand(X2,nand(X2,X2)) = nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X2)),nand(X2,X2)),
    inference(congruence,[status(thm)],[c216]) ).

cnf(c218,plain,
    nand(nand(X2,X2),nand(X2,nand(X2,X2))) = nand(nand(X2,X2),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X2)),nand(X2,X2))),
    inference(congruence,[status(thm)],[c217]) ).

cnf(c219,plain,
    nand(nand(nand(X2,X2),nand(X2,nand(X2,X2))),nand(nand(X,nand(nand(X2,X),X)),nand(X,nand(nand(X2,X),X)))) = nand(nand(nand(X2,X2),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X2)),nand(X2,X2))),nand(nand(X,nand(nand(X2,X),X)),nand(X,nand(nand(X2,X),X)))),
    inference(congruence,[status(thm)],[c218]) ).

cnf(c220,plain,
    nand(nand(nand(X2,X2),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X2)),nand(X2,X2))),nand(nand(X,nand(nand(X2,X),X)),nand(X,nand(nand(X2,X),X)))) = nand(X,nand(nand(X2,X),X)),
    inference(substitution,[status(thm)],[c95]) ).

cnf(c221,plain,
    nand(nand(nand(X2,X2),nand(X2,nand(X2,X2))),nand(nand(X,nand(nand(X2,X),X)),nand(X,nand(nand(X2,X),X)))) = nand(X,nand(nand(X2,X),X)),
    inference(transitivity,[status(thm)],[c219,c220]) ).

cnf(c222,plain,
    nand(X2,nand(nand(X,nand(nand(X2,X),X)),nand(X,nand(nand(X2,X),X)))) = nand(X,nand(nand(X2,X),X)),
    inference(transitivity,[status(thm)],[c214,c221]) ).

cnf(c223,plain,
    nand(nand(X2,X),nand(nand(nand(X2,nand(X2,X)),nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X)))),nand(nand(X2,nand(X2,X)),nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X)))))) = nand(nand(X2,nand(X2,X)),nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X)))),
    inference(substitution,[status(thm)],[c222]) ).

cnf(c224,plain,
    nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X))) = nand(X2,nand(X2,nand(X2,X))),
    inference(congruence,[status(thm)],[c198]) ).

cnf(c225,plain,
    nand(nand(X2,nand(X2,X)),nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X)))) = nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X)))),
    inference(congruence,[status(thm)],[c224]) ).

cnf(c226,plain,
    nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X)))) = X2,
    inference(substitution,[status(thm)],[c198]) ).

cnf(c227,plain,
    nand(nand(X2,nand(X2,X)),nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X)))) = X2,
    inference(transitivity,[status(thm)],[c225,c226]) ).

cnf(c228,plain,
    nand(nand(X2,X),nand(nand(nand(X2,nand(X2,X)),nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X)))),nand(nand(X2,nand(X2,X)),nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X)))))) = X2,
    inference(transitivity,[status(thm)],[c223,c227]) ).

cnf(c229,plain,
    nand(nand(X2,X),nand(nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X)))),nand(nand(X2,nand(X2,X)),nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X)))))) = X2,
    inference(transitivity,[status(thm)],[c212,c228]) ).

cnf(c230,plain,
    nand(nand(X2,X),nand(X2,nand(nand(X2,nand(X2,X)),nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X)))))) = X2,
    inference(transitivity,[status(thm)],[c207,c229]) ).

cnf(c231,plain,
    nand(nand(X2,X),nand(X2,nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X)))))) = X2,
    inference(transitivity,[status(thm)],[c203,c230]) ).

cnf(c232,plain,
    nand(nand(X2,X),nand(X2,X2)) = X2,
    inference(transitivity,[status(thm)],[c168,c231]) ).

cnf(c233,plain,
    nand(nand(X2,nand(nand(X,X2),X2)),nand(X2,X2)) = X2,
    inference(substitution,[status(thm)],[c232]) ).

cnf(c234,plain,
    nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X2,X2)),nand(X2,X2)) = nand(X2,nand(X2,X2)),
    inference(congruence,[status(thm)],[c233]) ).

cnf(c235,plain,
    nand(nand(X2,X2),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X2,X2)),nand(X2,X2))) = nand(nand(X2,X2),nand(X2,nand(X2,X2))),
    inference(congruence,[status(thm)],[c234]) ).

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

cnf(c237,plain,
    nand(nand(nand(X2,X2),nand(X2,nand(X2,X2))),X) = nand(X2,X),
    inference(congruence,[status(thm)],[c72]) ).

cnf(c238,plain,
    nand(nand(nand(X2,X2),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X2,X2)),nand(X2,X2))),X) = nand(X2,X),
    inference(transitivity,[status(thm)],[c236,c237]) ).

cnf(c239,plain,
    nand(X2,nand(nand(X,X2),X2)) = nand(X2,X),
    inference(transitivity,[status(thm)],[c9,c238]) ).

cnf(c240,plain,
    nand(X,nand(nand(X2,X),X)) = nand(X,X2),
    inference(substitution,[status(thm)],[c239]) ).

cnf(c241,plain,
    nand(X,X2) = nand(X,nand(nand(X2,X),X)),
    inference(symmetry,[status(thm)],[c240]) ).

cnf(c242,plain,
    nand(X2,X) = nand(X2,nand(nand(X,X2),X2)),
    inference(symmetry,[status(thm)],[c239]) ).

cnf(c243,plain,
    nand(nand(X2,X),X) = nand(nand(X2,nand(nand(X,X2),X2)),X),
    inference(congruence,[status(thm)],[c242]) ).

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

cnf(c245,plain,
    nand(X,nand(nand(X2,nand(nand(X,X2),X2)),X)) = nand(X2,nand(nand(X,X2),X2)),
    inference(substitution,[status(thm)],[c110]) ).

cnf(c246,plain,
    nand(X,nand(nand(X2,nand(nand(X,X2),X2)),X)) = nand(X2,X),
    inference(transitivity,[status(thm)],[c245,c239]) ).

cnf(c247,plain,
    nand(X,nand(nand(X2,X),X)) = nand(X2,X),
    inference(transitivity,[status(thm)],[c244,c246]) ).

cnf(c248,plain,
    nand(X,X2) = nand(X2,X),
    inference(transitivity,[status(thm)],[c241,c247]) ).

cnf(c249,plain,
    nand(nand(X3,nand(X2,X)),nand(X3,X2)) = nand(nand(X3,X2),nand(X3,nand(X2,X))),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c250,plain,
    nand(X3,nand(X2,X)) = nand(nand(X2,X),X3),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c251,plain,
    nand(nand(X3,X2),nand(X3,nand(X2,X))) = nand(nand(X3,X2),nand(nand(X2,X),X3)),
    inference(congruence,[status(thm)],[c250]) ).

cnf(c252,plain,
    nand(nand(X3,X2),nand(nand(X2,X),X3)) = nand(nand(nand(X2,X),X3),nand(X3,X2)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c253,plain,
    nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))) = nand(nand(X2,X),X3),
    inference(substitution,[status(thm)],[c239]) ).

cnf(c254,plain,
    nand(nand(X2,X),X3) = nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),
    inference(symmetry,[status(thm)],[c253]) ).

cnf(c255,plain,
    nand(nand(nand(X2,X),X3),nand(X3,X2)) = nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2)),
    inference(congruence,[status(thm)],[c254]) ).

cnf(c256,plain,
    nand(nand(nand(X2,X),nand(nand(X3,nand(X2,X)),nand(X2,X))),nand(X3,X2)) = X3,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c257,plain,
    nand(nand(nand(X2,X),X3),nand(X3,X2)) = X3,
    inference(transitivity,[status(thm)],[c255,c256]) ).

cnf(c258,plain,
    nand(nand(X3,X2),nand(nand(X2,X),X3)) = X3,
    inference(transitivity,[status(thm)],[c252,c257]) ).

cnf(c259,plain,
    nand(nand(X3,X2),nand(X3,nand(X2,X))) = X3,
    inference(transitivity,[status(thm)],[c251,c258]) ).

cnf(c260,plain,
    nand(nand(X3,nand(X2,X)),nand(X3,X2)) = X3,
    inference(transitivity,[status(thm)],[c249,c259]) ).

cnf(c261,plain,
    nand(nand(nand(nand(nand(X,X2),X2),X3),nand(X,X2)),nand(nand(nand(nand(X,X2),X2),X3),X)) = nand(nand(nand(X,X2),X2),X3),
    inference(substitution,[status(thm)],[c260]) ).

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

cnf(c263,plain,
    nand(nand(nand(nand(X2,X),X),X3),X2) = nand(X2,nand(nand(nand(X2,X),X),X3)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c264,plain,
    nand(nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(X2,X),X),X3)),nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(X2,X),X),X3))) = nand(nand(nand(X2,X),X),X3),
    inference(substitution,[status(thm)],[c64]) ).

cnf(c265,plain,
    nand(nand(nand(X2,X),X),X3) = nand(nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(X2,X),X),X3)),nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(X2,X),X),X3))),
    inference(symmetry,[status(thm)],[c264]) ).

cnf(c266,plain,
    nand(X2,nand(nand(nand(X2,X),X),X3)) = nand(X2,nand(nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(X2,X),X),X3)),nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(X2,X),X),X3)))),
    inference(congruence,[status(thm)],[c265]) ).

cnf(c267,plain,
    nand(X2,X) = nand(X,X2),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c268,plain,
    nand(X,nand(X2,X)) = nand(X,nand(X,X2)),
    inference(congruence,[status(thm)],[c267]) ).

cnf(c269,plain,
    nand(X2,nand(X,nand(X2,X))) = nand(X2,nand(X,nand(X,X2))),
    inference(congruence,[status(thm)],[c268]) ).

cnf(c270,plain,
    nand(X,nand(X,X2)) = nand(nand(X,X2),X),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c271,plain,
    nand(X2,nand(X,nand(X,X2))) = nand(X2,nand(nand(X,X2),X)),
    inference(congruence,[status(thm)],[c270]) ).

cnf(c272,plain,
    nand(X2,X) = nand(X,X2),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c273,plain,
    nand(X3,nand(X2,X)) = nand(X3,nand(X,X2)),
    inference(congruence,[status(thm)],[c272]) ).

cnf(c274,plain,
    nand(X2,nand(X3,nand(X2,X))) = nand(X2,nand(X3,nand(X,X2))),
    inference(congruence,[status(thm)],[c273]) ).

cnf(c275,plain,
    nand(X3,nand(X2,nand(X3,nand(X2,X)))) = nand(X3,nand(X2,nand(X3,nand(X,X2)))),
    inference(congruence,[status(thm)],[c274]) ).

cnf(c276,plain,
    nand(X2,nand(X3,nand(X,X2))) = nand(nand(X3,nand(X,X2)),X2),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c277,plain,
    nand(X3,nand(X2,nand(X3,nand(X,X2)))) = nand(X3,nand(nand(X3,nand(X,X2)),X2)),
    inference(congruence,[status(thm)],[c276]) ).

cnf(c278,plain,
    nand(X2,X) = nand(X2,nand(nand(X,X2),X2)),
    inference(symmetry,[status(thm)],[c239]) ).

cnf(c279,plain,
    nand(nand(X3,X2),nand(X2,nand(X,X3))) = nand(nand(X3,nand(nand(X2,X3),X3)),nand(X2,nand(X,X3))),
    inference(congruence,[status(thm)],[c278]) ).

cnf(c280,plain,
    nand(nand(X3,nand(nand(X2,X3),X3)),nand(X2,nand(X,X3))) = X2,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c281,plain,
    nand(nand(X3,X2),nand(X2,nand(X,X3))) = X2,
    inference(transitivity,[status(thm)],[c279,c280]) ).

cnf(c282,plain,
    nand(nand(X2,X3),nand(X3,nand(X,X2))) = X3,
    inference(substitution,[status(thm)],[c281]) ).

cnf(c283,plain,
    X3 = nand(nand(X2,X3),nand(X3,nand(X,X2))),
    inference(symmetry,[status(thm)],[c282]) ).

cnf(c284,plain,
    nand(nand(X4,nand(X2,X3)),X3) = nand(nand(X4,nand(X2,X3)),nand(nand(X2,X3),nand(X3,nand(X,X2)))),
    inference(congruence,[status(thm)],[c283]) ).

cnf(c285,plain,
    nand(X4,nand(nand(X4,nand(X2,X3)),X3)) = nand(X4,nand(nand(X4,nand(X2,X3)),nand(nand(X2,X3),nand(X3,nand(X,X2))))),
    inference(congruence,[status(thm)],[c284]) ).

cnf(c286,plain,
    nand(X2,X) = nand(X,X2),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c287,plain,
    nand(nand(X3,X2),nand(X2,X)) = nand(nand(X2,X3),nand(X2,X)),
    inference(congruence,[status(thm)],[c286]) ).

cnf(c288,plain,
    nand(X3,nand(nand(X3,X2),nand(X2,X))) = nand(X3,nand(nand(X2,X3),nand(X2,X))),
    inference(congruence,[status(thm)],[c287]) ).

cnf(c289,plain,
    nand(X2,X) = nand(X,X2),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c290,plain,
    nand(nand(X2,X3),nand(X2,X)) = nand(nand(X2,X3),nand(X,X2)),
    inference(congruence,[status(thm)],[c289]) ).

cnf(c291,plain,
    nand(X3,nand(nand(X2,X3),nand(X2,X))) = nand(X3,nand(nand(X2,X3),nand(X,X2))),
    inference(congruence,[status(thm)],[c290]) ).

cnf(c292,plain,
    nand(nand(X2,X3),nand(X,X2)) = nand(nand(X,X2),nand(X2,X3)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c293,plain,
    nand(X3,nand(nand(X2,X3),nand(X,X2))) = nand(X3,nand(nand(X,X2),nand(X2,X3))),
    inference(congruence,[status(thm)],[c292]) ).

cnf(c294,plain,
    nand(X3,nand(nand(X,X2),nand(X2,X3))) = nand(nand(nand(X,X2),nand(X2,X3)),X3),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c295,plain,
    nand(X,nand(nand(X2,X),X)) = nand(X,X2),
    inference(substitution,[status(thm)],[c239]) ).

cnf(c296,plain,
    nand(X,X2) = nand(X,nand(nand(X2,X),X)),
    inference(symmetry,[status(thm)],[c295]) ).

cnf(c297,plain,
    nand(nand(X,X2),nand(X2,X3)) = nand(nand(X,X2),nand(X2,nand(nand(X3,X2),X2))),
    inference(congruence,[status(thm)],[c296]) ).

cnf(c298,plain,
    nand(nand(nand(X,X2),nand(X2,X3)),X3) = nand(nand(nand(X,X2),nand(X2,nand(nand(X3,X2),X2))),X3),
    inference(congruence,[status(thm)],[c297]) ).

cnf(c299,plain,
    nand(nand(X,X2),nand(nand(nand(X2,nand(nand(X3,X2),X2)),nand(X,X2)),nand(X,X2))) = nand(nand(X,X2),nand(X2,nand(nand(X3,X2),X2))),
    inference(substitution,[status(thm)],[c239]) ).

cnf(c300,plain,
    nand(nand(X,X2),nand(X2,nand(nand(X3,X2),X2))) = nand(nand(X,X2),nand(nand(nand(X2,nand(nand(X3,X2),X2)),nand(X,X2)),nand(X,X2))),
    inference(symmetry,[status(thm)],[c299]) ).

cnf(c301,plain,
    nand(nand(nand(X,X2),nand(X2,nand(nand(X3,X2),X2))),X3) = nand(nand(nand(X,X2),nand(nand(nand(X2,nand(nand(X3,X2),X2)),nand(X,X2)),nand(X,X2))),X3),
    inference(congruence,[status(thm)],[c300]) ).

cnf(c302,plain,
    nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))) = X3,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c303,plain,
    X3 = nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))),
    inference(symmetry,[status(thm)],[c302]) ).

cnf(c304,plain,
    nand(nand(nand(X,X2),nand(nand(nand(X2,nand(nand(X3,X2),X2)),nand(X,X2)),nand(X,X2))),X3) = nand(nand(nand(X,X2),nand(nand(nand(X2,nand(nand(X3,X2),X2)),nand(X,X2)),nand(X,X2))),nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2)))),
    inference(congruence,[status(thm)],[c303]) ).

cnf(c305,plain,
    nand(nand(nand(X,X2),nand(nand(nand(X2,nand(nand(X3,X2),X2)),nand(X,X2)),nand(X,X2))),nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2)))) = nand(X2,nand(nand(X3,X2),X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c306,plain,
    nand(X,nand(nand(X2,X),X)) = nand(X,X2),
    inference(substitution,[status(thm)],[c239]) ).

cnf(c307,plain,
    nand(X2,X) = nand(X,X2),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c308,plain,
    nand(X,X2) = nand(X2,X),
    inference(symmetry,[status(thm)],[c307]) ).

cnf(c309,plain,
    nand(X,nand(nand(X2,X),X)) = nand(X2,X),
    inference(transitivity,[status(thm)],[c306,c308]) ).

cnf(c310,plain,
    nand(nand(nand(X,X2),nand(nand(nand(X2,nand(nand(X3,X2),X2)),nand(X,X2)),nand(X,X2))),nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2)))) = nand(X3,X2),
    inference(transitivity,[status(thm)],[c305,c309]) ).

cnf(c311,plain,
    nand(nand(nand(X,X2),nand(nand(nand(X2,nand(nand(X3,X2),X2)),nand(X,X2)),nand(X,X2))),X3) = nand(X3,X2),
    inference(transitivity,[status(thm)],[c304,c310]) ).

cnf(c312,plain,
    nand(nand(nand(X,X2),nand(X2,nand(nand(X3,X2),X2))),X3) = nand(X3,X2),
    inference(transitivity,[status(thm)],[c301,c311]) ).

cnf(c313,plain,
    nand(nand(nand(X,X2),nand(X2,X3)),X3) = nand(X3,X2),
    inference(transitivity,[status(thm)],[c298,c312]) ).

cnf(c314,plain,
    nand(X3,nand(nand(X,X2),nand(X2,X3))) = nand(X3,X2),
    inference(transitivity,[status(thm)],[c294,c313]) ).

cnf(c315,plain,
    nand(X3,nand(nand(X2,X3),nand(X,X2))) = nand(X3,X2),
    inference(transitivity,[status(thm)],[c293,c314]) ).

cnf(c316,plain,
    nand(X3,nand(nand(X2,X3),nand(X2,X))) = nand(X3,X2),
    inference(transitivity,[status(thm)],[c291,c315]) ).

cnf(c317,plain,
    nand(X3,nand(nand(X3,X2),nand(X2,X))) = nand(X3,X2),
    inference(transitivity,[status(thm)],[c288,c316]) ).

cnf(c318,plain,
    nand(X4,nand(nand(X4,nand(X2,X3)),nand(nand(X2,X3),nand(X3,nand(X,X2))))) = nand(X4,nand(X2,X3)),
    inference(substitution,[status(thm)],[c317]) ).

cnf(c319,plain,
    nand(X2,X) = nand(X,X2),
    inference(substitution,[status(thm)],[c248]) ).

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

cnf(c321,plain,
    nand(X3,nand(X,X2)) = nand(X3,nand(X2,X)),
    inference(congruence,[status(thm)],[c320]) ).

cnf(c322,plain,
    nand(X4,nand(nand(X4,nand(X2,X3)),nand(nand(X2,X3),nand(X3,nand(X,X2))))) = nand(X4,nand(X3,X2)),
    inference(transitivity,[status(thm)],[c318,c321]) ).

cnf(c323,plain,
    nand(X3,nand(nand(X3,nand(X,X2)),X2)) = nand(X3,nand(X2,X)),
    inference(transitivity,[status(thm)],[c285,c322]) ).

cnf(c324,plain,
    nand(X3,nand(X2,nand(X3,nand(X,X2)))) = nand(X3,nand(X2,X)),
    inference(transitivity,[status(thm)],[c277,c323]) ).

cnf(c325,plain,
    nand(X3,nand(X2,nand(X3,nand(X2,X)))) = nand(X3,nand(X2,X)),
    inference(transitivity,[status(thm)],[c275,c324]) ).

cnf(c326,plain,
    nand(X2,nand(nand(X,X2),nand(X2,nand(nand(X,X2),X)))) = nand(X2,nand(nand(X,X2),X)),
    inference(substitution,[status(thm)],[c325]) ).

cnf(c327,plain,
    nand(X2,nand(nand(X,X2),X)) = nand(X2,nand(nand(X,X2),nand(X2,nand(nand(X,X2),X)))),
    inference(symmetry,[status(thm)],[c326]) ).

cnf(c328,plain,
    nand(nand(X,X2),nand(X2,nand(nand(X,X2),X))) = X2,
    inference(substitution,[status(thm)],[c281]) ).

cnf(c329,plain,
    nand(X2,nand(nand(X,X2),nand(X2,nand(nand(X,X2),X)))) = nand(X2,X2),
    inference(congruence,[status(thm)],[c328]) ).

cnf(c330,plain,
    nand(X2,nand(nand(X,X2),X)) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c327,c329]) ).

cnf(c331,plain,
    nand(X2,nand(X,nand(X,X2))) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c271,c330]) ).

cnf(c332,plain,
    nand(X2,nand(X,nand(X2,X))) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c269,c331]) ).

cnf(c333,plain,
    nand(X,nand(X2,nand(X,X2))) = nand(X,X),
    inference(substitution,[status(thm)],[c332]) ).

cnf(c334,plain,
    nand(X,X) = nand(X,nand(X2,nand(X,X2))),
    inference(symmetry,[status(thm)],[c333]) ).

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

cnf(c336,plain,
    nand(X2,nand(X,nand(X2,nand(X,X2)))) = nand(X2,nand(X,X2)),
    inference(substitution,[status(thm)],[c325]) ).

cnf(c337,plain,
    nand(X2,X) = nand(X,X2),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c338,plain,
    nand(X,X2) = nand(X2,X),
    inference(symmetry,[status(thm)],[c337]) ).

cnf(c339,plain,
    nand(X2,nand(X,X2)) = nand(X2,nand(X2,X)),
    inference(congruence,[status(thm)],[c338]) ).

cnf(c340,plain,
    nand(X2,nand(X,nand(X2,nand(X,X2)))) = nand(X2,nand(X2,X)),
    inference(transitivity,[status(thm)],[c336,c339]) ).

cnf(c341,plain,
    nand(X2,nand(X,X)) = nand(X2,nand(X2,X)),
    inference(transitivity,[status(thm)],[c335,c340]) ).

cnf(c342,plain,
    nand(X2,nand(nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(X2,X),X),X3)),nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(X2,X),X),X3)))) = nand(X2,nand(X2,nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(X2,X),X),X3)))),
    inference(substitution,[status(thm)],[c341]) ).

cnf(c343,plain,
    nand(X3,nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X3,X2),X2),X))) = nand(nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X3,X2),X2),X)),X3),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c344,plain,
    nand(nand(X3,X2),nand(X,X2)) = nand(nand(X,X2),nand(X3,X2)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c345,plain,
    nand(nand(X2,X4),nand(nand(X4,X3),nand(X,X3))) = nand(nand(X2,X4),nand(nand(X,X3),nand(X4,X3))),
    inference(congruence,[status(thm)],[c344]) ).

cnf(c346,plain,
    nand(nand(X4,X3),nand(nand(X2,X4),nand(nand(X4,X3),nand(X,X3)))) = nand(nand(X4,X3),nand(nand(X2,X4),nand(nand(X,X3),nand(X4,X3)))),
    inference(congruence,[status(thm)],[c345]) ).

cnf(c347,plain,
    nand(nand(X2,X4),nand(nand(X,X3),nand(X4,X3))) = nand(nand(nand(X,X3),nand(X4,X3)),nand(X2,X4)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c348,plain,
    nand(nand(X4,X3),nand(nand(X2,X4),nand(nand(X,X3),nand(X4,X3)))) = nand(nand(X4,X3),nand(nand(nand(X,X3),nand(X4,X3)),nand(X2,X4))),
    inference(congruence,[status(thm)],[c347]) ).

cnf(c349,plain,
    nand(nand(X,X2),nand(nand(nand(X3,X2),nand(X,X2)),nand(X,X2))) = nand(nand(X,X2),nand(X3,X2)),
    inference(substitution,[status(thm)],[c239]) ).

cnf(c350,plain,
    nand(nand(X,X2),nand(X3,X2)) = nand(nand(X,X2),nand(nand(nand(X3,X2),nand(X,X2)),nand(X,X2))),
    inference(symmetry,[status(thm)],[c349]) ).

cnf(c351,plain,
    nand(nand(nand(X,X3),nand(X4,X3)),nand(X2,X4)) = nand(nand(nand(X,X3),nand(nand(nand(X4,X3),nand(X,X3)),nand(X,X3))),nand(X2,X4)),
    inference(congruence,[status(thm)],[c350]) ).

cnf(c352,plain,
    nand(nand(X4,X3),nand(nand(nand(X,X3),nand(X4,X3)),nand(X2,X4))) = nand(nand(X4,X3),nand(nand(nand(X,X3),nand(nand(nand(X4,X3),nand(X,X3)),nand(X,X3))),nand(X2,X4))),
    inference(congruence,[status(thm)],[c351]) ).

cnf(c353,plain,
    X = nand(nand(X,X),nand(X,nand(X,X))),
    inference(symmetry,[status(thm)],[c72]) ).

cnf(c354,plain,
    nand(X2,nand(nand(X2,X),X2)) = nand(nand(nand(X2,X2),nand(X2,nand(X2,X2))),nand(nand(X2,X),X2)),
    inference(congruence,[status(thm)],[c353]) ).

cnf(c355,plain,
    X2 = nand(nand(X2,X),nand(X2,X2)),
    inference(symmetry,[status(thm)],[c232]) ).

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

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

cnf(c358,plain,
    nand(nand(nand(X2,X2),nand(X2,nand(X2,X2))),nand(nand(X2,X),X2)) = nand(nand(nand(X2,X2),nand(nand(nand(X2,X),nand(X2,X2)),nand(X2,X2))),nand(nand(X2,X),X2)),
    inference(congruence,[status(thm)],[c357]) ).

cnf(c359,plain,
    nand(nand(nand(X2,X2),nand(nand(nand(X2,X),nand(X2,X2)),nand(X2,X2))),nand(nand(X2,X),X2)) = nand(X2,X),
    inference(substitution,[status(thm)],[c44]) ).

cnf(c360,plain,
    nand(nand(nand(X2,X2),nand(X2,nand(X2,X2))),nand(nand(X2,X),X2)) = nand(X2,X),
    inference(transitivity,[status(thm)],[c358,c359]) ).

cnf(c361,plain,
    nand(X2,nand(nand(X2,X),X2)) = nand(X2,X),
    inference(transitivity,[status(thm)],[c354,c360]) ).

cnf(c362,plain,
    nand(X2,X) = nand(X2,nand(nand(X2,X),X2)),
    inference(symmetry,[status(thm)],[c361]) ).

cnf(c363,plain,
    nand(nand(X4,X3),nand(nand(nand(X,X3),nand(nand(nand(X4,X3),nand(X,X3)),nand(X,X3))),nand(X2,X4))) = nand(nand(X4,nand(nand(X4,X3),X4)),nand(nand(nand(X,X3),nand(nand(nand(X4,X3),nand(X,X3)),nand(X,X3))),nand(X2,X4))),
    inference(congruence,[status(thm)],[c362]) ).

cnf(c364,plain,
    nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))) = nand(nand(X2,X),nand(X2,X)),
    inference(substitution,[status(thm)],[c57]) ).

cnf(c365,plain,
    nand(nand(X2,X),nand(X2,X)) = nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),
    inference(symmetry,[status(thm)],[c364]) ).

cnf(c366,plain,
    nand(nand(nand(X2,X),nand(X2,X)),X) = nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X),
    inference(congruence,[status(thm)],[c365]) ).

cnf(c367,plain,
    nand(nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(nand(X2,X),nand(X,nand(X2,X)))),nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(nand(X2,X),nand(X,nand(X2,X))))) = nand(nand(X2,X),nand(X,nand(X2,X))),
    inference(substitution,[status(thm)],[c64]) ).

cnf(c368,plain,
    nand(nand(X2,X),nand(X,nand(X2,X))) = nand(nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(nand(X2,X),nand(X,nand(X2,X)))),nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(nand(X2,X),nand(X,nand(X2,X))))),
    inference(symmetry,[status(thm)],[c367]) ).

cnf(c369,plain,
    nand(X,X) = nand(X,nand(nand(X,X),X)),
    inference(symmetry,[status(thm)],[c57]) ).

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

cnf(c371,plain,
    nand(X,X2) = nand(X2,nand(nand(nand(nand(X,X2),nand(X,X2)),X2),X2)),
    inference(symmetry,[status(thm)],[c192]) ).

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

cnf(c373,plain,
    nand(nand(X2,nand(nand(X2,X2),X2)),nand(X2,nand(nand(nand(nand(X,X2),nand(X,X2)),X2),X2))) = X2,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c374,plain,
    nand(nand(X2,nand(nand(X2,X2),X2)),nand(X,X2)) = X2,
    inference(transitivity,[status(thm)],[c372,c373]) ).

cnf(c375,plain,
    nand(nand(X2,X2),nand(X,X2)) = X2,
    inference(transitivity,[status(thm)],[c370,c374]) ).

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

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

cnf(c378,plain,
    nand(X,nand(X2,X)) = nand(nand(nand(X,X),nand(X2,X)),nand(X2,X)),
    inference(congruence,[status(thm)],[c377]) ).

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

cnf(c380,plain,
    nand(nand(nand(X3,X2),nand(X2,nand(X3,X2))),nand(nand(X,X2),nand(X2,nand(X,X2)))) = nand(nand(nand(X3,X2),nand(nand(nand(X2,X2),nand(X3,X2)),nand(X3,X2))),nand(nand(X,X2),nand(X2,nand(X,X2)))),
    inference(congruence,[status(thm)],[c379]) ).

cnf(c381,plain,
    nand(X,X) = nand(X,nand(nand(X,X),X)),
    inference(symmetry,[status(thm)],[c57]) ).

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

cnf(c383,plain,
    nand(nand(nand(X,X),nand(X2,X)),nand(X2,X)) = nand(nand(nand(X,nand(nand(X,X),X)),nand(X2,X)),nand(X2,X)),
    inference(congruence,[status(thm)],[c382]) ).

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

cnf(c385,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X2,X2),nand(X3,X2)),nand(X3,X2))),nand(nand(X,X2),nand(X2,nand(X,X2)))) = nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(X2,X2),X2)),nand(X3,X2)),nand(X3,X2))),nand(nand(X,X2),nand(X2,nand(X,X2)))),
    inference(congruence,[status(thm)],[c384]) ).

cnf(c386,plain,
    nand(X,nand(nand(nand(nand(X2,X),nand(X2,X)),X),X)) = nand(X2,X),
    inference(substitution,[status(thm)],[c192]) ).

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

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

cnf(c389,plain,
    nand(nand(X2,X),nand(X,nand(X2,X))) = nand(nand(X2,X),nand(X,nand(X,nand(nand(nand(nand(X2,X),nand(X2,X)),X),X)))),
    inference(congruence,[status(thm)],[c388]) ).

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

cnf(c391,plain,
    nand(X,nand(nand(nand(nand(X2,X),nand(X2,X)),X),X)) = nand(X2,X),
    inference(substitution,[status(thm)],[c192]) ).

cnf(c392,plain,
    nand(X2,X) = nand(X,nand(nand(nand(nand(X2,X),nand(X2,X)),X),X)),
    inference(symmetry,[status(thm)],[c391]) ).

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

cnf(c394,plain,
    nand(nand(nand(X2,X),nand(X,nand(X,nand(nand(nand(nand(X2,X),nand(X2,X)),X),X)))),X) = nand(nand(nand(X,nand(nand(nand(nand(X2,X),nand(X2,X)),X),X)),nand(X,nand(X,nand(nand(nand(nand(X2,X),nand(X2,X)),X),X)))),X),
    inference(congruence,[status(thm)],[c393]) ).

cnf(c395,plain,
    nand(nand(nand(X,nand(nand(nand(nand(X2,X),nand(X2,X)),X),X)),nand(X,nand(X,nand(nand(nand(nand(X2,X),nand(X2,X)),X),X)))),X) = nand(X,nand(nand(X,X),X)),
    inference(substitution,[status(thm)],[c52]) ).

cnf(c396,plain,
    nand(nand(nand(X,nand(nand(nand(nand(X2,X),nand(X2,X)),X),X)),nand(X,nand(X,nand(nand(nand(nand(X2,X),nand(X2,X)),X),X)))),X) = nand(X,X),
    inference(transitivity,[status(thm)],[c395,c57]) ).

cnf(c397,plain,
    nand(nand(nand(X2,X),nand(X,nand(X,nand(nand(nand(nand(X2,X),nand(X2,X)),X),X)))),X) = nand(X,X),
    inference(transitivity,[status(thm)],[c394,c396]) ).

cnf(c398,plain,
    nand(nand(nand(X2,X),nand(X,nand(X2,X))),X) = nand(X,X),
    inference(transitivity,[status(thm)],[c390,c397]) ).

cnf(c399,plain,
    nand(nand(nand(X,X2),nand(X2,nand(X,X2))),X2) = nand(X2,X2),
    inference(substitution,[status(thm)],[c398]) ).

cnf(c400,plain,
    nand(X2,X2) = nand(nand(nand(X,X2),nand(X2,nand(X,X2))),X2),
    inference(symmetry,[status(thm)],[c399]) ).

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

cnf(c402,plain,
    nand(X2,nand(nand(X2,X2),X2)) = nand(X2,nand(nand(nand(nand(X,X2),nand(X2,nand(X,X2))),X2),X2)),
    inference(congruence,[status(thm)],[c401]) ).

cnf(c403,plain,
    nand(nand(X2,nand(nand(X2,X2),X2)),nand(X3,X2)) = nand(nand(X2,nand(nand(nand(nand(X,X2),nand(X2,nand(X,X2))),X2),X2)),nand(X3,X2)),
    inference(congruence,[status(thm)],[c402]) ).

cnf(c404,plain,
    nand(nand(nand(X2,nand(nand(X2,X2),X2)),nand(X3,X2)),nand(X3,X2)) = nand(nand(nand(X2,nand(nand(nand(nand(X,X2),nand(X2,nand(X,X2))),X2),X2)),nand(X3,X2)),nand(X3,X2)),
    inference(congruence,[status(thm)],[c403]) ).

cnf(c405,plain,
    nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(X2,X2),X2)),nand(X3,X2)),nand(X3,X2))) = nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(nand(nand(X,X2),nand(X2,nand(X,X2))),X2),X2)),nand(X3,X2)),nand(X3,X2))),
    inference(congruence,[status(thm)],[c404]) ).

cnf(c406,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(X2,X2),X2)),nand(X3,X2)),nand(X3,X2))),nand(nand(X,X2),nand(X2,nand(X,X2)))) = nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(nand(nand(X,X2),nand(X2,nand(X,X2))),X2),X2)),nand(X3,X2)),nand(X3,X2))),nand(nand(X,X2),nand(X2,nand(X,X2)))),
    inference(congruence,[status(thm)],[c405]) ).

cnf(c407,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(nand(nand(X,X2),nand(X2,nand(X,X2))),X2),X2)),nand(X3,X2)),nand(X3,X2))),nand(nand(X,X2),nand(X2,nand(X,X2)))) = nand(X2,nand(nand(nand(nand(X,X2),nand(X2,nand(X,X2))),X2),X2)),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c408,plain,
    nand(nand(nand(X,X2),nand(X2,nand(X,X2))),X2) = nand(X2,X2),
    inference(substitution,[status(thm)],[c398]) ).

cnf(c409,plain,
    nand(nand(nand(nand(X,X2),nand(X2,nand(X,X2))),X2),X2) = nand(nand(X2,X2),X2),
    inference(congruence,[status(thm)],[c408]) ).

cnf(c410,plain,
    nand(X2,nand(nand(nand(nand(X,X2),nand(X2,nand(X,X2))),X2),X2)) = nand(X2,nand(nand(X2,X2),X2)),
    inference(congruence,[status(thm)],[c409]) ).

cnf(c411,plain,
    nand(X2,nand(nand(nand(nand(X,X2),nand(X2,nand(X,X2))),X2),X2)) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c410,c57]) ).

cnf(c412,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(nand(nand(X,X2),nand(X2,nand(X,X2))),X2),X2)),nand(X3,X2)),nand(X3,X2))),nand(nand(X,X2),nand(X2,nand(X,X2)))) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c407,c411]) ).

cnf(c413,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(X2,X2),X2)),nand(X3,X2)),nand(X3,X2))),nand(nand(X,X2),nand(X2,nand(X,X2)))) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c406,c412]) ).

cnf(c414,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X2,X2),nand(X3,X2)),nand(X3,X2))),nand(nand(X,X2),nand(X2,nand(X,X2)))) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c385,c413]) ).

cnf(c415,plain,
    nand(nand(nand(X3,X2),nand(X2,nand(X3,X2))),nand(nand(X,X2),nand(X2,nand(X,X2)))) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c380,c414]) ).

cnf(c416,plain,
    nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(nand(X2,X),nand(X,nand(X2,X)))) = nand(X,X),
    inference(substitution,[status(thm)],[c415]) ).

cnf(c417,plain,
    nand(nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(nand(X2,X),nand(X,nand(X2,X)))),nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(nand(X2,X),nand(X,nand(X2,X))))) = nand(nand(X,X),nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(nand(X2,X),nand(X,nand(X2,X))))),
    inference(congruence,[status(thm)],[c416]) ).

cnf(c418,plain,
    nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(nand(X2,X),nand(X,nand(X2,X)))) = nand(X,X),
    inference(substitution,[status(thm)],[c415]) ).

cnf(c419,plain,
    nand(nand(X,X),nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(nand(X2,X),nand(X,nand(X2,X))))) = nand(nand(X,X),nand(X,X)),
    inference(congruence,[status(thm)],[c418]) ).

cnf(c420,plain,
    nand(nand(X,X),nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(nand(X2,X),nand(X,nand(X2,X))))) = X,
    inference(transitivity,[status(thm)],[c419,c64]) ).

cnf(c421,plain,
    nand(nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(nand(X2,X),nand(X,nand(X2,X)))),nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(nand(X2,X),nand(X,nand(X2,X))))) = X,
    inference(transitivity,[status(thm)],[c417,c420]) ).

cnf(c422,plain,
    nand(nand(X2,X),nand(X,nand(X2,X))) = X,
    inference(transitivity,[status(thm)],[c368,c421]) ).

cnf(c423,plain,
    X = nand(nand(X2,X),nand(X,nand(X2,X))),
    inference(symmetry,[status(thm)],[c422]) ).

cnf(c424,plain,
    nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X) = nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),nand(nand(X2,X),nand(X,nand(X2,X)))),
    inference(congruence,[status(thm)],[c423]) ).

cnf(c425,plain,
    nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),nand(nand(X2,X),nand(X,nand(X2,X)))) = nand(X2,X),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c426,plain,
    nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X) = nand(X2,X),
    inference(transitivity,[status(thm)],[c424,c425]) ).

cnf(c427,plain,
    nand(nand(nand(X2,X),nand(X2,X)),X) = nand(X2,X),
    inference(transitivity,[status(thm)],[c366,c426]) ).

cnf(c428,plain,
    nand(nand(nand(X,X2),nand(X,X2)),X2) = nand(X,X2),
    inference(substitution,[status(thm)],[c427]) ).

cnf(c429,plain,
    nand(X,X2) = nand(nand(nand(X,X2),nand(X,X2)),X2),
    inference(symmetry,[status(thm)],[c428]) ).

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

cnf(c431,plain,
    nand(X2,nand(nand(X,X2),X2)) = nand(X2,nand(nand(nand(nand(X,X2),nand(X,X2)),X2),X2)),
    inference(congruence,[status(thm)],[c430]) ).

cnf(c432,plain,
    nand(X2,nand(nand(X,X2),X2)) = nand(X,X2),
    inference(transitivity,[status(thm)],[c431,c192]) ).

cnf(c433,plain,
    nand(X,X2) = nand(X2,nand(nand(X,X2),X2)),
    inference(symmetry,[status(thm)],[c432]) ).

cnf(c434,plain,
    nand(nand(X,X2),nand(X3,X2)) = nand(nand(X2,nand(nand(X,X2),X2)),nand(X3,X2)),
    inference(congruence,[status(thm)],[c433]) ).

cnf(c435,plain,
    nand(nand(nand(X,X2),nand(X3,X2)),nand(X3,X2)) = nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X3,X2)),nand(X3,X2)),
    inference(congruence,[status(thm)],[c434]) ).

cnf(c436,plain,
    nand(nand(X3,X2),nand(nand(nand(X,X2),nand(X3,X2)),nand(X3,X2))) = nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X3,X2)),nand(X3,X2))),
    inference(congruence,[status(thm)],[c435]) ).

cnf(c437,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X,X2),nand(X3,X2)),nand(X3,X2))),X) = nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X3,X2)),nand(X3,X2))),X),
    inference(congruence,[status(thm)],[c436]) ).

cnf(c438,plain,
    nand(nand(X2,nand(nand(X,X2),X2)),nand(X,nand(X3,X2))) = X,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c439,plain,
    X = nand(nand(X2,nand(nand(X,X2),X2)),nand(X,nand(X3,X2))),
    inference(symmetry,[status(thm)],[c438]) ).

cnf(c440,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X3,X2)),nand(X3,X2))),X) = nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X3,X2)),nand(X3,X2))),nand(nand(X2,nand(nand(X,X2),X2)),nand(X,nand(X3,X2)))),
    inference(congruence,[status(thm)],[c439]) ).

cnf(c441,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X3,X2)),nand(X3,X2))),nand(nand(X2,nand(nand(X,X2),X2)),nand(X,nand(X3,X2)))) = nand(X2,nand(nand(X,X2),X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c442,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X3,X2)),nand(X3,X2))),nand(nand(X2,nand(nand(X,X2),X2)),nand(X,nand(X3,X2)))) = nand(X,X2),
    inference(transitivity,[status(thm)],[c441,c432]) ).

cnf(c443,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(nand(X,X2),X2)),nand(X3,X2)),nand(X3,X2))),X) = nand(X,X2),
    inference(transitivity,[status(thm)],[c440,c442]) ).

cnf(c444,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X,X2),nand(X3,X2)),nand(X3,X2))),X) = nand(X,X2),
    inference(transitivity,[status(thm)],[c437,c443]) ).

cnf(c445,plain,
    nand(nand(nand(X,X2),nand(nand(nand(X3,X2),nand(X,X2)),nand(X,X2))),X3) = nand(X3,X2),
    inference(substitution,[status(thm)],[c444]) ).

cnf(c446,plain,
    nand(X3,X2) = nand(nand(nand(X,X2),nand(nand(nand(X3,X2),nand(X,X2)),nand(X,X2))),X3),
    inference(symmetry,[status(thm)],[c445]) ).

cnf(c447,plain,
    nand(nand(X3,X2),X3) = nand(nand(nand(nand(X,X2),nand(nand(nand(X3,X2),nand(X,X2)),nand(X,X2))),X3),X3),
    inference(congruence,[status(thm)],[c446]) ).

cnf(c448,plain,
    nand(X3,nand(nand(X3,X2),X3)) = nand(X3,nand(nand(nand(nand(X,X2),nand(nand(nand(X3,X2),nand(X,X2)),nand(X,X2))),X3),X3)),
    inference(congruence,[status(thm)],[c447]) ).

cnf(c449,plain,
    nand(nand(X4,nand(nand(X4,X3),X4)),nand(nand(nand(X,X3),nand(nand(nand(X4,X3),nand(X,X3)),nand(X,X3))),nand(X2,X4))) = nand(nand(X4,nand(nand(nand(nand(X,X3),nand(nand(nand(X4,X3),nand(X,X3)),nand(X,X3))),X4),X4)),nand(nand(nand(X,X3),nand(nand(nand(X4,X3),nand(X,X3)),nand(X,X3))),nand(X2,X4))),
    inference(congruence,[status(thm)],[c448]) ).

cnf(c450,plain,
    nand(nand(X4,nand(nand(nand(nand(X,X3),nand(nand(nand(X4,X3),nand(X,X3)),nand(X,X3))),X4),X4)),nand(nand(nand(X,X3),nand(nand(nand(X4,X3),nand(X,X3)),nand(X,X3))),nand(X2,X4))) = nand(nand(X,X3),nand(nand(nand(X4,X3),nand(X,X3)),nand(X,X3))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c451,plain,
    nand(nand(X,X2),nand(nand(nand(X3,X2),nand(X,X2)),nand(X,X2))) = nand(nand(X,X2),nand(X3,X2)),
    inference(substitution,[status(thm)],[c239]) ).

cnf(c452,plain,
    nand(nand(X3,X2),nand(X,X2)) = nand(nand(X,X2),nand(X3,X2)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c453,plain,
    nand(nand(X,X2),nand(X3,X2)) = nand(nand(X3,X2),nand(X,X2)),
    inference(symmetry,[status(thm)],[c452]) ).

cnf(c454,plain,
    nand(nand(X,X2),nand(nand(nand(X3,X2),nand(X,X2)),nand(X,X2))) = nand(nand(X3,X2),nand(X,X2)),
    inference(transitivity,[status(thm)],[c451,c453]) ).

cnf(c455,plain,
    nand(nand(X4,nand(nand(nand(nand(X,X3),nand(nand(nand(X4,X3),nand(X,X3)),nand(X,X3))),X4),X4)),nand(nand(nand(X,X3),nand(nand(nand(X4,X3),nand(X,X3)),nand(X,X3))),nand(X2,X4))) = nand(nand(X4,X3),nand(X,X3)),
    inference(transitivity,[status(thm)],[c450,c454]) ).

cnf(c456,plain,
    nand(nand(X4,nand(nand(X4,X3),X4)),nand(nand(nand(X,X3),nand(nand(nand(X4,X3),nand(X,X3)),nand(X,X3))),nand(X2,X4))) = nand(nand(X4,X3),nand(X,X3)),
    inference(transitivity,[status(thm)],[c449,c455]) ).

cnf(c457,plain,
    nand(nand(X4,X3),nand(nand(nand(X,X3),nand(nand(nand(X4,X3),nand(X,X3)),nand(X,X3))),nand(X2,X4))) = nand(nand(X4,X3),nand(X,X3)),
    inference(transitivity,[status(thm)],[c363,c456]) ).

cnf(c458,plain,
    nand(nand(X4,X3),nand(nand(nand(X,X3),nand(X4,X3)),nand(X2,X4))) = nand(nand(X4,X3),nand(X,X3)),
    inference(transitivity,[status(thm)],[c352,c457]) ).

cnf(c459,plain,
    nand(nand(X4,X3),nand(nand(X2,X4),nand(nand(X,X3),nand(X4,X3)))) = nand(nand(X4,X3),nand(X,X3)),
    inference(transitivity,[status(thm)],[c348,c458]) ).

cnf(c460,plain,
    nand(nand(X4,X3),nand(nand(X2,X4),nand(nand(X4,X3),nand(X,X3)))) = nand(nand(X4,X3),nand(X,X3)),
    inference(transitivity,[status(thm)],[c346,c459]) ).

cnf(c461,plain,
    nand(nand(X4,X3),nand(nand(X,X4),nand(nand(X4,X3),nand(nand(nand(X3,X2),X2),X3)))) = nand(nand(X4,X3),nand(nand(nand(X3,X2),X2),X3)),
    inference(substitution,[status(thm)],[c460]) ).

cnf(c462,plain,
    nand(nand(X4,X3),nand(nand(nand(X3,X2),X2),X3)) = nand(nand(X4,X3),nand(nand(X,X4),nand(nand(X4,X3),nand(nand(nand(X3,X2),X2),X3)))),
    inference(symmetry,[status(thm)],[c461]) ).

cnf(c463,plain,
    nand(nand(nand(X2,X),X),X2) = nand(X2,nand(nand(X2,X),X)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c464,plain,
    nand(nand(X2,X),X) = nand(X,nand(X2,X)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c465,plain,
    nand(X2,nand(nand(X2,X),X)) = nand(X2,nand(X,nand(X2,X))),
    inference(congruence,[status(thm)],[c464]) ).

cnf(c466,plain,
    nand(X2,nand(nand(X2,X),X)) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c465,c332]) ).

cnf(c467,plain,
    nand(nand(nand(X2,X),X),X2) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c463,c466]) ).

cnf(c468,plain,
    nand(nand(X3,X2),nand(nand(nand(X2,X),X),X2)) = nand(nand(X3,X2),nand(X2,X2)),
    inference(congruence,[status(thm)],[c467]) ).

cnf(c469,plain,
    nand(nand(X,X4),nand(nand(X4,X3),nand(nand(nand(X3,X2),X2),X3))) = nand(nand(X,X4),nand(nand(X4,X3),nand(X3,X3))),
    inference(congruence,[status(thm)],[c468]) ).

cnf(c470,plain,
    nand(nand(X4,X3),nand(nand(X,X4),nand(nand(X4,X3),nand(nand(nand(X3,X2),X2),X3)))) = nand(nand(X4,X3),nand(nand(X,X4),nand(nand(X4,X3),nand(X3,X3)))),
    inference(congruence,[status(thm)],[c469]) ).

cnf(c471,plain,
    nand(nand(X3,X2),nand(nand(X,X3),nand(nand(X3,X2),nand(X2,X2)))) = nand(nand(X3,X2),nand(X2,X2)),
    inference(substitution,[status(thm)],[c460]) ).

cnf(c472,plain,
    nand(X2,X) = nand(X2,nand(nand(X2,X),X2)),
    inference(symmetry,[status(thm)],[c361]) ).

cnf(c473,plain,
    nand(nand(X2,X),nand(X,X)) = nand(nand(X2,nand(nand(X2,X),X2)),nand(X,X)),
    inference(congruence,[status(thm)],[c472]) ).

cnf(c474,plain,
    nand(X2,X) = nand(X,X2),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c475,plain,
    nand(nand(X2,X),X2) = nand(nand(X,X2),X2),
    inference(congruence,[status(thm)],[c474]) ).

cnf(c476,plain,
    nand(X2,nand(nand(X2,X),X2)) = nand(X2,nand(nand(X,X2),X2)),
    inference(congruence,[status(thm)],[c475]) ).

cnf(c477,plain,
    nand(nand(X2,nand(nand(X2,X),X2)),nand(X,X)) = nand(nand(X2,nand(nand(X,X2),X2)),nand(X,X)),
    inference(congruence,[status(thm)],[c476]) ).

cnf(c478,plain,
    nand(nand(X2,nand(nand(X2,X),X2)),nand(X,X)) = X,
    inference(transitivity,[status(thm)],[c477,c95]) ).

cnf(c479,plain,
    nand(nand(X2,X),nand(X,X)) = X,
    inference(transitivity,[status(thm)],[c473,c478]) ).

cnf(c480,plain,
    nand(nand(X3,X2),nand(nand(X,X3),nand(nand(X3,X2),nand(X2,X2)))) = X2,
    inference(transitivity,[status(thm)],[c471,c479]) ).

cnf(c481,plain,
    nand(nand(X4,X3),nand(nand(X,X4),nand(nand(X4,X3),nand(nand(nand(X3,X2),X2),X3)))) = X3,
    inference(transitivity,[status(thm)],[c470,c480]) ).

cnf(c482,plain,
    nand(nand(X3,X2),nand(nand(nand(X2,X),X),X2)) = X2,
    inference(transitivity,[status(thm)],[c462,c481]) ).

cnf(c483,plain,
    nand(nand(X2,X3),nand(nand(nand(X3,X),X),X3)) = X3,
    inference(substitution,[status(thm)],[c482]) ).

cnf(c484,plain,
    X3 = nand(nand(X2,X3),nand(nand(nand(X3,X),X),X3)),
    inference(symmetry,[status(thm)],[c483]) ).

cnf(c485,plain,
    nand(nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2)),X4) = nand(nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2)),nand(nand(X2,X4),nand(nand(nand(X4,X),X),X4))),
    inference(congruence,[status(thm)],[c484]) ).

cnf(c486,plain,
    nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X,X3),X),nand(nand(nand(nand(X3,X2),X2),X),nand(nand(X,X3),X)))) = nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X3,X2),X2),X)),
    inference(substitution,[status(thm)],[c332]) ).

cnf(c487,plain,
    nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X3,X2),X2),X)) = nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X,X3),X),nand(nand(nand(nand(X3,X2),X2),X),nand(nand(X,X3),X)))),
    inference(symmetry,[status(thm)],[c486]) ).

cnf(c488,plain,
    nand(nand(nand(X3,X2),X2),X) = nand(X,nand(nand(X3,X2),X2)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c489,plain,
    nand(nand(nand(nand(X3,X2),X2),X),nand(nand(X,X3),X)) = nand(nand(X,nand(nand(X3,X2),X2)),nand(nand(X,X3),X)),
    inference(congruence,[status(thm)],[c488]) ).

cnf(c490,plain,
    nand(X3,nand(nand(nand(X2,X),X),X2)) = nand(X3,nand(X2,X2)),
    inference(congruence,[status(thm)],[c467]) ).

cnf(c491,plain,
    nand(nand(X2,X),X2) = nand(X2,nand(X2,X)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c492,plain,
    nand(X2,nand(X2,X)) = nand(nand(X2,X),X2),
    inference(symmetry,[status(thm)],[c491]) ).

cnf(c493,plain,
    nand(X2,nand(X,X)) = nand(nand(X2,X),X2),
    inference(transitivity,[status(thm)],[c341,c492]) ).

cnf(c494,plain,
    nand(X3,nand(nand(nand(X2,X),X),X2)) = nand(nand(X3,X2),X3),
    inference(transitivity,[status(thm)],[c490,c493]) ).

cnf(c495,plain,
    nand(nand(X3,X2),X3) = nand(X3,nand(nand(nand(X2,X),X),X2)),
    inference(symmetry,[status(thm)],[c494]) ).

cnf(c496,plain,
    nand(nand(nand(X2,X),X),nand(nand(X3,X2),X3)) = nand(nand(nand(X2,X),X),nand(X3,nand(nand(nand(X2,X),X),X2))),
    inference(congruence,[status(thm)],[c495]) ).

cnf(c497,plain,
    nand(X3,nand(nand(nand(X2,X),X),nand(nand(X3,X2),X3))) = nand(X3,nand(nand(nand(X2,X),X),nand(X3,nand(nand(nand(X2,X),X),X2)))),
    inference(congruence,[status(thm)],[c496]) ).

cnf(c498,plain,
    nand(X3,nand(nand(nand(X2,X),X),nand(X3,nand(nand(nand(X2,X),X),X2)))) = nand(X3,nand(nand(nand(X2,X),X),X2)),
    inference(substitution,[status(thm)],[c325]) ).

cnf(c499,plain,
    nand(X3,nand(nand(nand(X2,X),X),nand(X3,nand(nand(nand(X2,X),X),X2)))) = nand(nand(X3,X2),X3),
    inference(transitivity,[status(thm)],[c498,c494]) ).

cnf(c500,plain,
    nand(X3,nand(nand(nand(X2,X),X),nand(nand(X3,X2),X3))) = nand(nand(X3,X2),X3),
    inference(transitivity,[status(thm)],[c497,c499]) ).

cnf(c501,plain,
    nand(X,nand(nand(nand(X3,X2),X2),nand(nand(X,X3),X))) = nand(nand(X,X3),X),
    inference(substitution,[status(thm)],[c500]) ).

cnf(c502,plain,
    nand(nand(X,X3),X) = nand(X,nand(nand(nand(X3,X2),X2),nand(nand(X,X3),X))),
    inference(symmetry,[status(thm)],[c501]) ).

cnf(c503,plain,
    nand(nand(X,nand(nand(X3,X2),X2)),nand(nand(X,X3),X)) = nand(nand(X,nand(nand(X3,X2),X2)),nand(X,nand(nand(nand(X3,X2),X2),nand(nand(X,X3),X)))),
    inference(congruence,[status(thm)],[c502]) ).

cnf(c504,plain,
    nand(X4,nand(X3,nand(X2,X))) = nand(nand(X3,nand(X2,X)),X4),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c505,plain,
    nand(nand(X4,X3),nand(X4,nand(X3,nand(X2,X)))) = nand(nand(X4,X3),nand(nand(X3,nand(X2,X)),X4)),
    inference(congruence,[status(thm)],[c504]) ).

cnf(c506,plain,
    nand(nand(X4,X3),nand(nand(X3,nand(X2,X)),X4)) = nand(nand(nand(X3,nand(X2,X)),X4),nand(X4,X3)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c507,plain,
    nand(nand(X,X3),nand(X3,nand(X2,X))) = X3,
    inference(substitution,[status(thm)],[c281]) ).

cnf(c508,plain,
    X3 = nand(nand(X,X3),nand(X3,nand(X2,X))),
    inference(symmetry,[status(thm)],[c507]) ).

cnf(c509,plain,
    nand(X4,X3) = nand(X4,nand(nand(X,X3),nand(X3,nand(X2,X)))),
    inference(congruence,[status(thm)],[c508]) ).

cnf(c510,plain,
    nand(nand(nand(X3,nand(X2,X)),X4),nand(X4,X3)) = nand(nand(nand(X3,nand(X2,X)),X4),nand(X4,nand(nand(X,X3),nand(X3,nand(X2,X))))),
    inference(congruence,[status(thm)],[c509]) ).

cnf(c511,plain,
    nand(nand(nand(X3,nand(X2,X)),X4),nand(X4,nand(nand(X,X3),nand(X3,nand(X2,X))))) = X4,
    inference(substitution,[status(thm)],[c281]) ).

cnf(c512,plain,
    nand(nand(nand(X3,nand(X2,X)),X4),nand(X4,X3)) = X4,
    inference(transitivity,[status(thm)],[c510,c511]) ).

cnf(c513,plain,
    nand(nand(X4,X3),nand(nand(X3,nand(X2,X)),X4)) = X4,
    inference(transitivity,[status(thm)],[c506,c512]) ).

cnf(c514,plain,
    nand(nand(X4,X3),nand(X4,nand(X3,nand(X2,X)))) = X4,
    inference(transitivity,[status(thm)],[c505,c513]) ).

cnf(c515,plain,
    nand(nand(X,nand(nand(X3,X2),X2)),nand(X,nand(nand(nand(X3,X2),X2),nand(nand(X,X3),X)))) = X,
    inference(substitution,[status(thm)],[c514]) ).

cnf(c516,plain,
    nand(nand(X,nand(nand(X3,X2),X2)),nand(nand(X,X3),X)) = X,
    inference(transitivity,[status(thm)],[c503,c515]) ).

cnf(c517,plain,
    nand(nand(nand(nand(X3,X2),X2),X),nand(nand(X,X3),X)) = X,
    inference(transitivity,[status(thm)],[c489,c516]) ).

cnf(c518,plain,
    nand(nand(nand(X,X3),X),nand(nand(nand(nand(X3,X2),X2),X),nand(nand(X,X3),X))) = nand(nand(nand(X,X3),X),X),
    inference(congruence,[status(thm)],[c517]) ).

cnf(c519,plain,
    nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X,X3),X),nand(nand(nand(nand(X3,X2),X2),X),nand(nand(X,X3),X)))) = nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X,X3),X),X)),
    inference(congruence,[status(thm)],[c518]) ).

cnf(c520,plain,
    nand(X,nand(nand(X2,X),X)) = nand(X2,X),
    inference(substitution,[status(thm)],[c432]) ).

cnf(c521,plain,
    nand(X2,X) = nand(X,nand(nand(X2,X),X)),
    inference(symmetry,[status(thm)],[c520]) ).

cnf(c522,plain,
    nand(nand(X3,X2),nand(X3,nand(X,X2))) = nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))),
    inference(congruence,[status(thm)],[c521]) ).

cnf(c523,plain,
    nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))) = X3,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c524,plain,
    nand(nand(X3,X2),nand(X3,nand(X,X2))) = X3,
    inference(transitivity,[status(thm)],[c522,c523]) ).

cnf(c525,plain,
    nand(nand(X2,X),nand(X2,nand(X2,X))) = X2,
    inference(substitution,[status(thm)],[c524]) ).

cnf(c526,plain,
    X2 = nand(nand(X2,X),nand(X2,nand(X2,X))),
    inference(symmetry,[status(thm)],[c525]) ).

cnf(c527,plain,
    nand(nand(nand(X2,X),X2),X2) = nand(nand(nand(X2,X),X2),nand(nand(X2,X),nand(X2,nand(X2,X)))),
    inference(congruence,[status(thm)],[c526]) ).

cnf(c528,plain,
    nand(nand(X2,X),X2) = nand(X2,nand(X2,X)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c529,plain,
    nand(nand(nand(X2,X),X2),nand(nand(X2,X),nand(X2,nand(X2,X)))) = nand(nand(X2,nand(X2,X)),nand(nand(X2,X),nand(X2,nand(X2,X)))),
    inference(congruence,[status(thm)],[c528]) ).

cnf(c530,plain,
    nand(nand(X2,nand(X2,X)),nand(nand(X2,X),nand(X2,nand(X2,X)))) = nand(X2,X),
    inference(substitution,[status(thm)],[c422]) ).

cnf(c531,plain,
    nand(nand(nand(X2,X),X2),nand(nand(X2,X),nand(X2,nand(X2,X)))) = nand(X2,X),
    inference(transitivity,[status(thm)],[c529,c530]) ).

cnf(c532,plain,
    nand(nand(nand(X2,X),X2),X2) = nand(X2,X),
    inference(transitivity,[status(thm)],[c527,c531]) ).

cnf(c533,plain,
    nand(nand(nand(X,X2),X),X) = nand(X,X2),
    inference(substitution,[status(thm)],[c532]) ).

cnf(c534,plain,
    nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X,X3),X),X)) = nand(nand(nand(nand(X3,X2),X2),X),nand(X,X3)),
    inference(congruence,[status(thm)],[c533]) ).

cnf(c535,plain,
    nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X,X3),X),nand(nand(nand(nand(X3,X2),X2),X),nand(nand(X,X3),X)))) = nand(nand(nand(nand(X3,X2),X2),X),nand(X,X3)),
    inference(transitivity,[status(thm)],[c519,c534]) ).

cnf(c536,plain,
    nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X3,X2),X2),X)) = nand(nand(nand(nand(X3,X2),X2),X),nand(X,X3)),
    inference(transitivity,[status(thm)],[c487,c535]) ).

cnf(c537,plain,
    nand(nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2)),nand(nand(X2,X4),nand(X,X4))) = nand(nand(nand(nand(nand(X4,X3),X3),X2),nand(X2,X4)),nand(nand(X2,X4),nand(X,X4))),
    inference(congruence,[status(thm)],[c536]) ).

cnf(c538,plain,
    nand(nand(nand(nand(X3,X2),X2),X),nand(X,X3)) = nand(nand(X,X3),nand(nand(nand(X3,X2),X2),X)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c539,plain,
    nand(nand(nand(nand(nand(X4,X3),X3),X2),nand(X2,X4)),nand(nand(X2,X4),nand(X,X4))) = nand(nand(nand(X2,X4),nand(nand(nand(X4,X3),X3),X2)),nand(nand(X2,X4),nand(X,X4))),
    inference(congruence,[status(thm)],[c538]) ).

cnf(c540,plain,
    nand(nand(X2,X4),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(X2,X4),nand(X,X4)))) = nand(nand(X2,X4),nand(X,X4)),
    inference(substitution,[status(thm)],[c460]) ).

cnf(c541,plain,
    nand(nand(X2,X4),nand(X,X4)) = nand(nand(X2,X4),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(X2,X4),nand(X,X4)))),
    inference(symmetry,[status(thm)],[c540]) ).

cnf(c542,plain,
    nand(nand(nand(X2,X4),nand(nand(nand(X4,X3),X3),X2)),nand(nand(X2,X4),nand(X,X4))) = nand(nand(nand(X2,X4),nand(nand(nand(X4,X3),X3),X2)),nand(nand(X2,X4),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(X2,X4),nand(X,X4))))),
    inference(congruence,[status(thm)],[c541]) ).

cnf(c543,plain,
    nand(nand(nand(X2,X4),nand(nand(nand(X4,X3),X3),X2)),nand(nand(X2,X4),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(X2,X4),nand(X,X4))))) = nand(X2,X4),
    inference(substitution,[status(thm)],[c514]) ).

cnf(c544,plain,
    nand(nand(nand(X2,X4),nand(nand(nand(X4,X3),X3),X2)),nand(nand(X2,X4),nand(X,X4))) = nand(X2,X4),
    inference(transitivity,[status(thm)],[c542,c543]) ).

cnf(c545,plain,
    nand(nand(nand(nand(nand(X4,X3),X3),X2),nand(X2,X4)),nand(nand(X2,X4),nand(X,X4))) = nand(X2,X4),
    inference(transitivity,[status(thm)],[c539,c544]) ).

cnf(c546,plain,
    nand(nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2)),nand(nand(X2,X4),nand(X,X4))) = nand(X2,X4),
    inference(transitivity,[status(thm)],[c537,c545]) ).

cnf(c547,plain,
    nand(nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2)),nand(nand(X2,X4),nand(nand(nand(X4,X),X),X4))) = nand(X2,X4),
    inference(substitution,[status(thm)],[c546]) ).

cnf(c548,plain,
    nand(nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X3,X2),X2),X)),X3) = nand(X,X3),
    inference(transitivity,[status(thm)],[c485,c547]) ).

cnf(c549,plain,
    nand(X3,nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X3,X2),X2),X))) = nand(X,X3),
    inference(transitivity,[status(thm)],[c343,c548]) ).

cnf(c550,plain,
    nand(X2,nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(X2,X),X),X3))) = nand(X3,X2),
    inference(substitution,[status(thm)],[c549]) ).

cnf(c551,plain,
    nand(X2,nand(X2,nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(X2,X),X),X3)))) = nand(X2,nand(X3,X2)),
    inference(congruence,[status(thm)],[c550]) ).

cnf(c552,plain,
    nand(nand(X2,X),X) = nand(X,nand(X2,X)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c553,plain,
    nand(X,nand(X2,X)) = nand(nand(X2,X),X),
    inference(symmetry,[status(thm)],[c552]) ).

cnf(c554,plain,
    nand(X2,nand(X2,nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(X2,X),X),X3)))) = nand(nand(X3,X2),X2),
    inference(transitivity,[status(thm)],[c551,c553]) ).

cnf(c555,plain,
    nand(X2,nand(nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(X2,X),X),X3)),nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(X2,X),X),X3)))) = nand(nand(X3,X2),X2),
    inference(transitivity,[status(thm)],[c342,c554]) ).

cnf(c556,plain,
    nand(X2,nand(nand(nand(X2,X),X),X3)) = nand(nand(X3,X2),X2),
    inference(transitivity,[status(thm)],[c266,c555]) ).

cnf(c557,plain,
    nand(nand(nand(nand(X2,X),X),X3),X2) = nand(nand(X3,X2),X2),
    inference(transitivity,[status(thm)],[c263,c556]) ).

cnf(c558,plain,
    nand(nand(X2,X),X) = nand(X,nand(X2,X)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c559,plain,
    nand(X3,nand(nand(X2,nand(X,nand(X2,X3))),nand(X2,nand(X,nand(X2,X3))))) = nand(nand(nand(X2,nand(X,nand(X2,X3))),nand(X2,nand(X,nand(X2,X3)))),X3),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c560,plain,
    nand(nand(nand(X,nand(X3,X2)),nand(nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(X,nand(X3,X2))),nand(X,nand(X3,X2)))),nand(X3,nand(X,nand(X3,X2)))) = nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c561,plain,
    nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))) = nand(nand(nand(X,nand(X3,X2)),nand(nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(X,nand(X3,X2))),nand(X,nand(X3,X2)))),nand(X3,nand(X,nand(X3,X2)))),
    inference(symmetry,[status(thm)],[c560]) ).

cnf(c562,plain,
    nand(nand(X,nand(X2,X)),nand(X,nand(X,nand(X2,X)))) = X,
    inference(substitution,[status(thm)],[c198]) ).

cnf(c563,plain,
    X = nand(nand(X,nand(X2,X)),nand(X,nand(X,nand(X2,X)))),
    inference(symmetry,[status(thm)],[c562]) ).

cnf(c564,plain,
    nand(X2,nand(X3,X)) = nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X2,nand(X3,X2)))),nand(X3,X)),
    inference(congruence,[status(thm)],[c563]) ).

cnf(c565,plain,
    nand(nand(X3,X2),nand(X2,nand(X3,X))) = nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X2,nand(X3,X2)))),nand(X3,X))),
    inference(congruence,[status(thm)],[c564]) ).

cnf(c566,plain,
    X = nand(nand(X2,X),nand(X,nand(X2,X))),
    inference(symmetry,[status(thm)],[c422]) ).

cnf(c567,plain,
    nand(X,nand(X,nand(X2,X))) = nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(X,nand(X2,X))),
    inference(congruence,[status(thm)],[c566]) ).

cnf(c568,plain,
    nand(nand(X,nand(X2,X)),nand(X,nand(X,nand(X2,X)))) = nand(nand(X,nand(X2,X)),nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(X,nand(X2,X)))),
    inference(congruence,[status(thm)],[c567]) ).

cnf(c569,plain,
    nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X2,nand(X3,X2)))),nand(X3,X)) = nand(nand(nand(X2,nand(X3,X2)),nand(nand(nand(X3,X2),nand(X2,nand(X3,X2))),nand(X2,nand(X3,X2)))),nand(X3,X)),
    inference(congruence,[status(thm)],[c568]) ).

cnf(c570,plain,
    nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X2,nand(X3,X2)))),nand(X3,X))) = nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(nand(nand(X3,X2),nand(X2,nand(X3,X2))),nand(X2,nand(X3,X2)))),nand(X3,X))),
    inference(congruence,[status(thm)],[c569]) ).

cnf(c571,plain,
    nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))) = nand(nand(X2,X),nand(X2,X)),
    inference(substitution,[status(thm)],[c57]) ).

cnf(c572,plain,
    nand(nand(X2,X),nand(X2,X)) = nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),
    inference(symmetry,[status(thm)],[c571]) ).

cnf(c573,plain,
    nand(nand(nand(X2,X),nand(X2,X)),X2) = nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2),
    inference(congruence,[status(thm)],[c572]) ).

cnf(c574,plain,
    X2 = nand(nand(X2,X),nand(X2,nand(X2,X))),
    inference(symmetry,[status(thm)],[c198]) ).

cnf(c575,plain,
    nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2) = nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),nand(nand(X2,X),nand(X2,nand(X2,X)))),
    inference(congruence,[status(thm)],[c574]) ).

cnf(c576,plain,
    nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),nand(nand(X2,X),nand(X2,nand(X2,X)))) = nand(X2,X),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c577,plain,
    nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2) = nand(X2,X),
    inference(transitivity,[status(thm)],[c575,c576]) ).

cnf(c578,plain,
    nand(nand(nand(X2,X),nand(X2,X)),X2) = nand(X2,X),
    inference(transitivity,[status(thm)],[c573,c577]) ).

cnf(c579,plain,
    nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X) = nand(X,nand(X2,X)),
    inference(substitution,[status(thm)],[c578]) ).

cnf(c580,plain,
    nand(X,nand(X2,X)) = nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X),
    inference(symmetry,[status(thm)],[c579]) ).

cnf(c581,plain,
    nand(nand(X2,X),nand(X,nand(X2,X))) = nand(nand(X2,X),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)),
    inference(congruence,[status(thm)],[c580]) ).

cnf(c582,plain,
    nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(X,nand(X2,X))) = nand(nand(nand(X2,X),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)),nand(X,nand(X2,X))),
    inference(congruence,[status(thm)],[c581]) ).

cnf(c583,plain,
    nand(nand(X,nand(X2,X)),nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(X,nand(X2,X)))) = nand(nand(X,nand(X2,X)),nand(nand(nand(X2,X),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)),nand(X,nand(X2,X)))),
    inference(congruence,[status(thm)],[c582]) ).

cnf(c584,plain,
    nand(nand(nand(X2,nand(X3,X2)),nand(nand(nand(X3,X2),nand(X2,nand(X3,X2))),nand(X2,nand(X3,X2)))),nand(X3,X)) = nand(nand(nand(X2,nand(X3,X2)),nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2)),nand(X2,nand(X3,X2)))),nand(X3,X)),
    inference(congruence,[status(thm)],[c583]) ).

cnf(c585,plain,
    nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(nand(nand(X3,X2),nand(X2,nand(X3,X2))),nand(X2,nand(X3,X2)))),nand(X3,X))) = nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2)),nand(X2,nand(X3,X2)))),nand(X3,X))),
    inference(congruence,[status(thm)],[c584]) ).

cnf(c586,plain,
    nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X) = nand(X,nand(X2,X)),
    inference(substitution,[status(thm)],[c578]) ).

cnf(c587,plain,
    nand(X,nand(X2,X)) = nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X),
    inference(symmetry,[status(thm)],[c586]) ).

cnf(c588,plain,
    nand(nand(nand(X2,X),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)),nand(X,nand(X2,X))) = nand(nand(nand(X2,X),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)),
    inference(congruence,[status(thm)],[c587]) ).

cnf(c589,plain,
    nand(nand(X,nand(X2,X)),nand(nand(nand(X2,X),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)),nand(X,nand(X2,X)))) = nand(nand(X,nand(X2,X)),nand(nand(nand(X2,X),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X))),
    inference(congruence,[status(thm)],[c588]) ).

cnf(c590,plain,
    nand(nand(nand(X2,nand(X3,X2)),nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2)),nand(X2,nand(X3,X2)))),nand(X3,X)) = nand(nand(nand(X2,nand(X3,X2)),nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2)),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2))),nand(X3,X)),
    inference(congruence,[status(thm)],[c589]) ).

cnf(c591,plain,
    nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2)),nand(X2,nand(X3,X2)))),nand(X3,X))) = nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2)),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2))),nand(X3,X))),
    inference(congruence,[status(thm)],[c590]) ).

cnf(c592,plain,
    nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X) = nand(X,nand(X2,X)),
    inference(substitution,[status(thm)],[c578]) ).

cnf(c593,plain,
    nand(X,nand(X2,X)) = nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X),
    inference(symmetry,[status(thm)],[c592]) ).

cnf(c594,plain,
    nand(nand(X,nand(X2,X)),nand(nand(nand(X2,X),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X))) = nand(nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X),nand(nand(nand(X2,X),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X))),
    inference(congruence,[status(thm)],[c593]) ).

cnf(c595,plain,
    nand(nand(nand(X2,nand(X3,X2)),nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2)),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2))),nand(X3,X)) = nand(nand(nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2),nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2)),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2))),nand(X3,X)),
    inference(congruence,[status(thm)],[c594]) ).

cnf(c596,plain,
    nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2)),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2))),nand(X3,X))) = nand(nand(X3,X2),nand(nand(nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2),nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2)),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2))),nand(X3,X))),
    inference(congruence,[status(thm)],[c595]) ).

cnf(c597,plain,
    nand(X2,X) = nand(X2,nand(nand(X2,X),X2)),
    inference(symmetry,[status(thm)],[c361]) ).

cnf(c598,plain,
    nand(nand(X4,X3),nand(nand(nand(X2,X3),nand(nand(nand(X4,X3),nand(X2,X3)),nand(X2,X3))),nand(X4,X))) = nand(nand(X4,nand(nand(X4,X3),X4)),nand(nand(nand(X2,X3),nand(nand(nand(X4,X3),nand(X2,X3)),nand(X2,X3))),nand(X4,X))),
    inference(congruence,[status(thm)],[c597]) ).

cnf(c599,plain,
    nand(nand(nand(X,X2),nand(nand(nand(X3,X2),nand(X,X2)),nand(X,X2))),X3) = nand(X3,X2),
    inference(substitution,[status(thm)],[c444]) ).

cnf(c600,plain,
    nand(X3,X2) = nand(nand(nand(X,X2),nand(nand(nand(X3,X2),nand(X,X2)),nand(X,X2))),X3),
    inference(symmetry,[status(thm)],[c599]) ).

cnf(c601,plain,
    nand(nand(X3,X2),X3) = nand(nand(nand(nand(X,X2),nand(nand(nand(X3,X2),nand(X,X2)),nand(X,X2))),X3),X3),
    inference(congruence,[status(thm)],[c600]) ).

cnf(c602,plain,
    nand(X3,nand(nand(X3,X2),X3)) = nand(X3,nand(nand(nand(nand(X,X2),nand(nand(nand(X3,X2),nand(X,X2)),nand(X,X2))),X3),X3)),
    inference(congruence,[status(thm)],[c601]) ).

cnf(c603,plain,
    nand(nand(X4,nand(nand(X4,X3),X4)),nand(nand(nand(X2,X3),nand(nand(nand(X4,X3),nand(X2,X3)),nand(X2,X3))),nand(X4,X))) = nand(nand(X4,nand(nand(nand(nand(X2,X3),nand(nand(nand(X4,X3),nand(X2,X3)),nand(X2,X3))),X4),X4)),nand(nand(nand(X2,X3),nand(nand(nand(X4,X3),nand(X2,X3)),nand(X2,X3))),nand(X4,X))),
    inference(congruence,[status(thm)],[c602]) ).

cnf(c604,plain,
    nand(X,nand(nand(X2,X),X)) = nand(X2,X),
    inference(substitution,[status(thm)],[c432]) ).

cnf(c605,plain,
    nand(X2,X) = nand(X,nand(nand(X2,X),X)),
    inference(symmetry,[status(thm)],[c604]) ).

cnf(c606,plain,
    nand(X2,nand(X3,X)) = nand(X2,nand(X,nand(nand(X3,X),X))),
    inference(congruence,[status(thm)],[c605]) ).

cnf(c607,plain,
    nand(nand(X3,nand(nand(X2,X3),X3)),nand(X2,nand(X3,X))) = nand(nand(X3,nand(nand(X2,X3),X3)),nand(X2,nand(X,nand(nand(X3,X),X)))),
    inference(congruence,[status(thm)],[c606]) ).

cnf(c608,plain,
    nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))) = X3,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c609,plain,
    X3 = nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))),
    inference(symmetry,[status(thm)],[c608]) ).

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

cnf(c611,plain,
    nand(nand(X3,X4),X4) = nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4),
    inference(congruence,[status(thm)],[c610]) ).

cnf(c612,plain,
    nand(X4,nand(nand(X3,X4),X4)) = nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4)),
    inference(congruence,[status(thm)],[c611]) ).

cnf(c613,plain,
    nand(nand(X4,nand(nand(X3,X4),X4)),nand(X3,nand(X2,nand(nand(X4,X2),X2)))) = nand(nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4)),nand(X3,nand(X2,nand(nand(X4,X2),X2)))),
    inference(congruence,[status(thm)],[c612]) ).

cnf(c614,plain,
    nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))) = X3,
    inference(substitution,[status(thm)],[c2]) ).

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

cnf(c616,plain,
    nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4) = nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),
    inference(congruence,[status(thm)],[c615]) ).

cnf(c617,plain,
    nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4)) = nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),
    inference(congruence,[status(thm)],[c616]) ).

cnf(c618,plain,
    nand(nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4)),nand(X3,nand(X2,nand(nand(X4,X2),X2)))) = nand(nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X3,nand(X2,nand(nand(X4,X2),X2)))),
    inference(congruence,[status(thm)],[c617]) ).

cnf(c619,plain,
    nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))) = X3,
    inference(substitution,[status(thm)],[c2]) ).

cnf(c620,plain,
    X3 = nand(nand(X2,nand(nand(X3,X2),X2)),nand(X3,nand(X,X2))),
    inference(symmetry,[status(thm)],[c619]) ).

cnf(c621,plain,
    nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))) = nand(nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))),nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),
    inference(congruence,[status(thm)],[c620]) ).

cnf(c622,plain,
    nand(nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X3,nand(X2,nand(nand(X4,X2),X2)))) = nand(nand(nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))),nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X3,nand(X2,nand(nand(X4,X2),X2)))),
    inference(congruence,[status(thm)],[c621]) ).

cnf(c623,plain,
    nand(nand(nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))),nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X3,nand(X2,nand(nand(X4,X2),X2)))) = X3,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c624,plain,
    nand(nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2))))),nand(X3,nand(X2,nand(nand(X4,X2),X2)))) = X3,
    inference(transitivity,[status(thm)],[c622,c623]) ).

cnf(c625,plain,
    nand(nand(X4,nand(nand(X3,nand(nand(X2,nand(nand(X4,X2),X2)),nand(X4,nand(X,X2)))),X4)),nand(X3,nand(X2,nand(nand(X4,X2),X2)))) = X3,
    inference(transitivity,[status(thm)],[c618,c624]) ).

cnf(c626,plain,
    nand(nand(X3,nand(nand(X2,X3),X3)),nand(X2,nand(X,nand(nand(X3,X),X)))) = X2,
    inference(transitivity,[status(thm)],[c613,c625]) ).

cnf(c627,plain,
    nand(nand(X3,nand(nand(X2,X3),X3)),nand(X2,nand(X3,X))) = X2,
    inference(transitivity,[status(thm)],[c607,c626]) ).

cnf(c628,plain,
    nand(nand(X4,nand(nand(nand(nand(X2,X3),nand(nand(nand(X4,X3),nand(X2,X3)),nand(X2,X3))),X4),X4)),nand(nand(nand(X2,X3),nand(nand(nand(X4,X3),nand(X2,X3)),nand(X2,X3))),nand(X4,X))) = nand(nand(X2,X3),nand(nand(nand(X4,X3),nand(X2,X3)),nand(X2,X3))),
    inference(substitution,[status(thm)],[c627]) ).

cnf(c629,plain,
    nand(nand(X4,nand(nand(X4,X3),X4)),nand(nand(nand(X2,X3),nand(nand(nand(X4,X3),nand(X2,X3)),nand(X2,X3))),nand(X4,X))) = nand(nand(X2,X3),nand(nand(nand(X4,X3),nand(X2,X3)),nand(X2,X3))),
    inference(transitivity,[status(thm)],[c603,c628]) ).

cnf(c630,plain,
    nand(nand(X4,X3),nand(nand(nand(X2,X3),nand(nand(nand(X4,X3),nand(X2,X3)),nand(X2,X3))),nand(X4,X))) = nand(nand(X2,X3),nand(nand(nand(X4,X3),nand(X2,X3)),nand(X2,X3))),
    inference(transitivity,[status(thm)],[c598,c629]) ).

cnf(c631,plain,
    nand(nand(X3,X2),nand(nand(nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2),nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2)),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2))),nand(X3,X))) = nand(nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2),nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2)),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2))),
    inference(substitution,[status(thm)],[c630]) ).

cnf(c632,plain,
    nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X) = nand(X,nand(X2,X)),
    inference(substitution,[status(thm)],[c578]) ).

cnf(c633,plain,
    nand(nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X),nand(nand(nand(X2,X),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X))) = nand(nand(X,nand(X2,X)),nand(nand(nand(X2,X),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X))),
    inference(congruence,[status(thm)],[c632]) ).

cnf(c634,plain,
    nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X) = nand(X,nand(X2,X)),
    inference(substitution,[status(thm)],[c578]) ).

cnf(c635,plain,
    nand(nand(X2,X),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)) = nand(nand(X2,X),nand(X,nand(X2,X))),
    inference(congruence,[status(thm)],[c634]) ).

cnf(c636,plain,
    nand(nand(nand(X2,X),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)) = nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)),
    inference(congruence,[status(thm)],[c635]) ).

cnf(c637,plain,
    nand(nand(X,nand(X2,X)),nand(nand(nand(X2,X),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X))) = nand(nand(X,nand(X2,X)),nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X))),
    inference(congruence,[status(thm)],[c636]) ).

cnf(c638,plain,
    nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X) = nand(X,nand(X2,X)),
    inference(substitution,[status(thm)],[c578]) ).

cnf(c639,plain,
    nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)) = nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(X,nand(X2,X))),
    inference(congruence,[status(thm)],[c638]) ).

cnf(c640,plain,
    nand(nand(X,nand(X2,X)),nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X))) = nand(nand(X,nand(X2,X)),nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(X,nand(X2,X)))),
    inference(congruence,[status(thm)],[c639]) ).

cnf(c641,plain,
    nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(X,nand(X2,X))) = nand(X,nand(X,nand(X2,X))),
    inference(congruence,[status(thm)],[c422]) ).

cnf(c642,plain,
    nand(nand(X,nand(X2,X)),nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(X,nand(X2,X)))) = nand(nand(X,nand(X2,X)),nand(X,nand(X,nand(X2,X)))),
    inference(congruence,[status(thm)],[c641]) ).

cnf(c643,plain,
    nand(nand(X,nand(X2,X)),nand(X,nand(X,nand(X2,X)))) = X,
    inference(substitution,[status(thm)],[c198]) ).

cnf(c644,plain,
    nand(nand(X,nand(X2,X)),nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(X,nand(X2,X)))) = X,
    inference(transitivity,[status(thm)],[c642,c643]) ).

cnf(c645,plain,
    nand(nand(X,nand(X2,X)),nand(nand(nand(X2,X),nand(X,nand(X2,X))),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X))) = X,
    inference(transitivity,[status(thm)],[c640,c644]) ).

cnf(c646,plain,
    nand(nand(X,nand(X2,X)),nand(nand(nand(X2,X),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X))) = X,
    inference(transitivity,[status(thm)],[c637,c645]) ).

cnf(c647,plain,
    nand(nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X),nand(nand(nand(X2,X),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X)),nand(nand(nand(X,nand(X2,X)),nand(X,nand(X2,X))),X))) = X,
    inference(transitivity,[status(thm)],[c633,c646]) ).

cnf(c648,plain,
    nand(nand(X3,X2),nand(nand(nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2),nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2)),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2))),nand(X3,X))) = X2,
    inference(transitivity,[status(thm)],[c631,c647]) ).

cnf(c649,plain,
    nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2)),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2))),nand(X3,X))) = X2,
    inference(transitivity,[status(thm)],[c596,c648]) ).

cnf(c650,plain,
    nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X3,X2))),X2)),nand(X2,nand(X3,X2)))),nand(X3,X))) = X2,
    inference(transitivity,[status(thm)],[c591,c649]) ).

cnf(c651,plain,
    nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(nand(nand(X3,X2),nand(X2,nand(X3,X2))),nand(X2,nand(X3,X2)))),nand(X3,X))) = X2,
    inference(transitivity,[status(thm)],[c585,c650]) ).

cnf(c652,plain,
    nand(nand(X3,X2),nand(nand(nand(X2,nand(X3,X2)),nand(X2,nand(X2,nand(X3,X2)))),nand(X3,X))) = X2,
    inference(transitivity,[status(thm)],[c570,c651]) ).

cnf(c653,plain,
    nand(nand(X3,X2),nand(X2,nand(X3,X))) = X2,
    inference(transitivity,[status(thm)],[c565,c652]) ).

cnf(c654,plain,
    nand(nand(X3,X),nand(X,nand(X3,X2))) = X,
    inference(substitution,[status(thm)],[c653]) ).

cnf(c655,plain,
    X = nand(nand(X3,X),nand(X,nand(X3,X2))),
    inference(symmetry,[status(thm)],[c654]) ).

cnf(c656,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X3,X),nand(X3,X2)),nand(X3,X2))),X) = nand(nand(nand(X3,X2),nand(nand(nand(X3,X),nand(X3,X2)),nand(X3,X2))),nand(nand(X3,X),nand(X,nand(X3,X2)))),
    inference(congruence,[status(thm)],[c655]) ).

cnf(c657,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X3,X),nand(X3,X2)),nand(X3,X2))),nand(nand(X3,X),nand(X,nand(X3,X2)))) = nand(X3,X),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c658,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X3,X),nand(X3,X2)),nand(X3,X2))),X) = nand(X3,X),
    inference(transitivity,[status(thm)],[c656,c657]) ).

cnf(c659,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(X,nand(X3,X2))) = nand(X3,nand(X,nand(X3,X2))),
    inference(substitution,[status(thm)],[c658]) ).

cnf(c660,plain,
    nand(nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(X,nand(X3,X2))),nand(X,nand(X3,X2))) = nand(nand(X3,nand(X,nand(X3,X2))),nand(X,nand(X3,X2))),
    inference(congruence,[status(thm)],[c659]) ).

cnf(c661,plain,
    nand(nand(X,nand(X3,X2)),nand(nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(X,nand(X3,X2))),nand(X,nand(X3,X2)))) = nand(nand(X,nand(X3,X2)),nand(nand(X3,nand(X,nand(X3,X2))),nand(X,nand(X3,X2)))),
    inference(congruence,[status(thm)],[c660]) ).

cnf(c662,plain,
    nand(nand(nand(X,nand(X3,X2)),nand(nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(X,nand(X3,X2))),nand(X,nand(X3,X2)))),nand(X3,nand(X,nand(X3,X2)))) = nand(nand(nand(X,nand(X3,X2)),nand(nand(X3,nand(X,nand(X3,X2))),nand(X,nand(X3,X2)))),nand(X3,nand(X,nand(X3,X2)))),
    inference(congruence,[status(thm)],[c661]) ).

cnf(c663,plain,
    nand(nand(X,nand(X3,X2)),nand(nand(X3,nand(X,nand(X3,X2))),nand(X,nand(X3,X2)))) = nand(X3,nand(X,nand(X3,X2))),
    inference(substitution,[status(thm)],[c432]) ).

cnf(c664,plain,
    nand(nand(nand(X,nand(X3,X2)),nand(nand(X3,nand(X,nand(X3,X2))),nand(X,nand(X3,X2)))),nand(X3,nand(X,nand(X3,X2)))) = nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,nand(X,nand(X3,X2)))),
    inference(congruence,[status(thm)],[c663]) ).

cnf(c665,plain,
    nand(nand(nand(X,nand(X3,X2)),nand(nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(X,nand(X3,X2))),nand(X,nand(X3,X2)))),nand(X3,nand(X,nand(X3,X2)))) = nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,nand(X,nand(X3,X2)))),
    inference(transitivity,[status(thm)],[c662,c664]) ).

cnf(c666,plain,
    nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))) = nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,nand(X,nand(X3,X2)))),
    inference(transitivity,[status(thm)],[c561,c665]) ).

cnf(c667,plain,
    nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X))) = nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))),
    inference(substitution,[status(thm)],[c666]) ).

cnf(c668,plain,
    nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))) = nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X))),
    inference(symmetry,[status(thm)],[c667]) ).

cnf(c669,plain,
    nand(nand(nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X))),nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X)))),nand(X3,X)) = nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X))),
    inference(substitution,[status(thm)],[c578]) ).

cnf(c670,plain,
    nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X))) = nand(nand(nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X))),nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X)))),nand(X3,X)),
    inference(symmetry,[status(thm)],[c669]) ).

cnf(c671,plain,
    nand(nand(X2,nand(X,X3)),nand(nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),nand(X2,nand(X,X3)))) = nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),
    inference(substitution,[status(thm)],[c110]) ).

cnf(c672,plain,
    nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)) = nand(nand(X2,nand(X,X3)),nand(nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),nand(X2,nand(X,X3)))),
    inference(symmetry,[status(thm)],[c671]) ).

cnf(c673,plain,
    nand(nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3))) = nand(nand(nand(X2,nand(X,X3)),nand(nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),nand(X2,nand(X,X3)))),nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3))),
    inference(congruence,[status(thm)],[c672]) ).

cnf(c674,plain,
    nand(nand(nand(X,X3),nand(nand(nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),nand(X,X3)),nand(X,X3))),nand(X2,nand(X,X3))) = nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c675,plain,
    nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)) = nand(nand(nand(X,X3),nand(nand(nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),nand(X,X3)),nand(X,X3))),nand(X2,nand(X,X3))),
    inference(symmetry,[status(thm)],[c674]) ).

cnf(c676,plain,
    nand(nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),nand(X2,nand(X,X3))) = nand(nand(nand(nand(X,X3),nand(nand(nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),nand(X,X3)),nand(X,X3))),nand(X2,nand(X,X3))),nand(X2,nand(X,X3))),
    inference(congruence,[status(thm)],[c675]) ).

cnf(c677,plain,
    nand(nand(X2,nand(X,X3)),nand(nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),nand(X2,nand(X,X3)))) = nand(nand(X2,nand(X,X3)),nand(nand(nand(nand(X,X3),nand(nand(nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),nand(X,X3)),nand(X,X3))),nand(X2,nand(X,X3))),nand(X2,nand(X,X3)))),
    inference(congruence,[status(thm)],[c676]) ).

cnf(c678,plain,
    nand(nand(nand(X2,nand(X,X3)),nand(nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),nand(X2,nand(X,X3)))),nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3))) = nand(nand(nand(X2,nand(X,X3)),nand(nand(nand(nand(X,X3),nand(nand(nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),nand(X,X3)),nand(X,X3))),nand(X2,nand(X,X3))),nand(X2,nand(X,X3)))),nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3))),
    inference(congruence,[status(thm)],[c677]) ).

cnf(c679,plain,
    nand(nand(nand(X2,nand(X,X3)),nand(nand(nand(nand(X,X3),nand(nand(nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),nand(X,X3)),nand(X,X3))),nand(X2,nand(X,X3))),nand(X2,nand(X,X3)))),nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3))) = nand(nand(X,X3),nand(nand(nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),nand(X,X3)),nand(X,X3))),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c680,plain,
    nand(nand(nand(X2,nand(X,X3)),nand(nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),nand(X2,nand(X,X3)))),nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3))) = nand(nand(X,X3),nand(nand(nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),nand(X,X3)),nand(X,X3))),
    inference(transitivity,[status(thm)],[c678,c679]) ).

cnf(c681,plain,
    nand(nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3))) = nand(nand(X,X3),nand(nand(nand(X3,nand(nand(nand(X2,nand(X,X3)),X3),X3)),nand(X,X3)),nand(X,X3))),
    inference(transitivity,[status(thm)],[c673,c680]) ).

cnf(c682,plain,
    nand(nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X))),nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X)))) = nand(nand(X2,nand(X3,X)),nand(nand(nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X))),nand(X2,nand(X3,X))),nand(X2,nand(X3,X)))),
    inference(substitution,[status(thm)],[c681]) ).

cnf(c683,plain,
    nand(nand(nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X))),nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X)))),nand(X3,X)) = nand(nand(nand(X2,nand(X3,X)),nand(nand(nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X))),nand(X2,nand(X3,X))),nand(X2,nand(X3,X)))),nand(X3,X)),
    inference(congruence,[status(thm)],[c682]) ).

cnf(c684,plain,
    nand(nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X))),nand(X2,nand(X3,X))) = nand(X3,nand(X2,nand(X3,X))),
    inference(substitution,[status(thm)],[c658]) ).

cnf(c685,plain,
    nand(nand(nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X))),nand(X2,nand(X3,X))),nand(X2,nand(X3,X))) = nand(nand(X3,nand(X2,nand(X3,X))),nand(X2,nand(X3,X))),
    inference(congruence,[status(thm)],[c684]) ).

cnf(c686,plain,
    nand(nand(X2,nand(X3,X)),nand(nand(nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X))),nand(X2,nand(X3,X))),nand(X2,nand(X3,X)))) = nand(nand(X2,nand(X3,X)),nand(nand(X3,nand(X2,nand(X3,X))),nand(X2,nand(X3,X)))),
    inference(congruence,[status(thm)],[c685]) ).

cnf(c687,plain,
    nand(nand(nand(X2,nand(X3,X)),nand(nand(nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X))),nand(X2,nand(X3,X))),nand(X2,nand(X3,X)))),nand(X3,X)) = nand(nand(nand(X2,nand(X3,X)),nand(nand(X3,nand(X2,nand(X3,X))),nand(X2,nand(X3,X)))),nand(X3,X)),
    inference(congruence,[status(thm)],[c686]) ).

cnf(c688,plain,
    nand(nand(X2,nand(X3,X)),nand(nand(X3,nand(X2,nand(X3,X))),nand(X2,nand(X3,X)))) = nand(X3,nand(X2,nand(X3,X))),
    inference(substitution,[status(thm)],[c432]) ).

cnf(c689,plain,
    nand(nand(nand(X2,nand(X3,X)),nand(nand(X3,nand(X2,nand(X3,X))),nand(X2,nand(X3,X)))),nand(X3,X)) = nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),
    inference(congruence,[status(thm)],[c688]) ).

cnf(c690,plain,
    nand(nand(nand(X2,nand(X3,X)),nand(nand(nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X))),nand(X2,nand(X3,X))),nand(X2,nand(X3,X)))),nand(X3,X)) = nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),
    inference(transitivity,[status(thm)],[c687,c689]) ).

cnf(c691,plain,
    nand(nand(nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X))),nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X)))),nand(X3,X)) = nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),
    inference(transitivity,[status(thm)],[c683,c690]) ).

cnf(c692,plain,
    nand(nand(X3,X),nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),nand(X3,X))) = nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),
    inference(transitivity,[status(thm)],[c670,c691]) ).

cnf(c693,plain,
    nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))) = nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,X)),
    inference(transitivity,[status(thm)],[c668,c692]) ).

cnf(c694,plain,
    nand(nand(X2,nand(X,nand(X2,X3))),nand(X2,nand(X,nand(X2,X3)))) = nand(nand(X2,nand(X,nand(X2,X3))),nand(X2,X3)),
    inference(substitution,[status(thm)],[c693]) ).

cnf(c695,plain,
    nand(nand(nand(X2,nand(X,nand(X2,X3))),nand(X2,nand(X,nand(X2,X3)))),X3) = nand(nand(nand(X2,nand(X,nand(X2,X3))),nand(X2,X3)),X3),
    inference(congruence,[status(thm)],[c694]) ).

cnf(c696,plain,
    nand(nand(X2,nand(X,nand(X2,X3))),nand(nand(nand(X2,X3),nand(X2,nand(X,nand(X2,X3)))),nand(X2,nand(X,nand(X2,X3))))) = nand(nand(X2,nand(X,nand(X2,X3))),nand(X2,X3)),
    inference(substitution,[status(thm)],[c239]) ).

cnf(c697,plain,
    nand(nand(X2,nand(X,nand(X2,X3))),nand(X2,X3)) = nand(nand(X2,nand(X,nand(X2,X3))),nand(nand(nand(X2,X3),nand(X2,nand(X,nand(X2,X3)))),nand(X2,nand(X,nand(X2,X3))))),
    inference(symmetry,[status(thm)],[c696]) ).

cnf(c698,plain,
    nand(nand(nand(X2,nand(X,nand(X2,X3))),nand(X2,X3)),X3) = nand(nand(nand(X2,nand(X,nand(X2,X3))),nand(nand(nand(X2,X3),nand(X2,nand(X,nand(X2,X3)))),nand(X2,nand(X,nand(X2,X3))))),X3),
    inference(congruence,[status(thm)],[c697]) ).

cnf(c699,plain,
    nand(nand(X2,X3),nand(X3,nand(X2,nand(X,nand(X2,X3))))) = X3,
    inference(substitution,[status(thm)],[c653]) ).

cnf(c700,plain,
    X3 = nand(nand(X2,X3),nand(X3,nand(X2,nand(X,nand(X2,X3))))),
    inference(symmetry,[status(thm)],[c699]) ).

cnf(c701,plain,
    nand(nand(nand(X2,nand(X,nand(X2,X3))),nand(nand(nand(X2,X3),nand(X2,nand(X,nand(X2,X3)))),nand(X2,nand(X,nand(X2,X3))))),X3) = nand(nand(nand(X2,nand(X,nand(X2,X3))),nand(nand(nand(X2,X3),nand(X2,nand(X,nand(X2,X3)))),nand(X2,nand(X,nand(X2,X3))))),nand(nand(X2,X3),nand(X3,nand(X2,nand(X,nand(X2,X3)))))),
    inference(congruence,[status(thm)],[c700]) ).

cnf(c702,plain,
    nand(nand(nand(X2,nand(X,nand(X2,X3))),nand(nand(nand(X2,X3),nand(X2,nand(X,nand(X2,X3)))),nand(X2,nand(X,nand(X2,X3))))),nand(nand(X2,X3),nand(X3,nand(X2,nand(X,nand(X2,X3)))))) = nand(X2,X3),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c703,plain,
    nand(nand(nand(X2,nand(X,nand(X2,X3))),nand(nand(nand(X2,X3),nand(X2,nand(X,nand(X2,X3)))),nand(X2,nand(X,nand(X2,X3))))),X3) = nand(X2,X3),
    inference(transitivity,[status(thm)],[c701,c702]) ).

cnf(c704,plain,
    nand(nand(nand(X2,nand(X,nand(X2,X3))),nand(X2,X3)),X3) = nand(X2,X3),
    inference(transitivity,[status(thm)],[c698,c703]) ).

cnf(c705,plain,
    nand(nand(nand(X2,nand(X,nand(X2,X3))),nand(X2,nand(X,nand(X2,X3)))),X3) = nand(X2,X3),
    inference(transitivity,[status(thm)],[c695,c704]) ).

cnf(c706,plain,
    nand(X3,nand(nand(X2,nand(X,nand(X2,X3))),nand(X2,nand(X,nand(X2,X3))))) = nand(X2,X3),
    inference(transitivity,[status(thm)],[c559,c705]) ).

cnf(c707,plain,
    nand(X,nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X))))) = nand(X3,X),
    inference(substitution,[status(thm)],[c706]) ).

cnf(c708,plain,
    nand(X3,X) = nand(X,nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X))))),
    inference(symmetry,[status(thm)],[c707]) ).

cnf(c709,plain,
    nand(X,nand(X3,X)) = nand(X,nand(X,nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))))),
    inference(congruence,[status(thm)],[c708]) ).

cnf(c710,plain,
    nand(X,nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))),nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))))) = nand(X,nand(X,nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))))),
    inference(substitution,[status(thm)],[c341]) ).

cnf(c711,plain,
    nand(X,nand(X,nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))))) = nand(X,nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))),nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))))),
    inference(symmetry,[status(thm)],[c710]) ).

cnf(c712,plain,
    nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))),nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X))))) = nand(X3,nand(X2,nand(X3,X))),
    inference(substitution,[status(thm)],[c64]) ).

cnf(c713,plain,
    nand(X,nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))),nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))))) = nand(X,nand(X3,nand(X2,nand(X3,X)))),
    inference(congruence,[status(thm)],[c712]) ).

cnf(c714,plain,
    nand(nand(X3,nand(X2,nand(X3,X))),X) = nand(X,nand(X3,nand(X2,nand(X3,X)))),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c715,plain,
    nand(X,nand(X3,nand(X2,nand(X3,X)))) = nand(nand(X3,nand(X2,nand(X3,X))),X),
    inference(symmetry,[status(thm)],[c714]) ).

cnf(c716,plain,
    nand(X,nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))),nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))))) = nand(nand(X3,nand(X2,nand(X3,X))),X),
    inference(transitivity,[status(thm)],[c713,c715]) ).

cnf(c717,plain,
    nand(X,nand(X,nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))))) = nand(nand(X3,nand(X2,nand(X3,X))),X),
    inference(transitivity,[status(thm)],[c711,c716]) ).

cnf(c718,plain,
    nand(X,nand(X3,X)) = nand(nand(X3,nand(X2,nand(X3,X))),X),
    inference(transitivity,[status(thm)],[c709,c717]) ).

cnf(c719,plain,
    nand(nand(X3,X),X) = nand(nand(X3,nand(X2,nand(X3,X))),X),
    inference(transitivity,[status(thm)],[c558,c718]) ).

cnf(c720,plain,
    nand(nand(nand(nand(X2,X),X),X4),X2) = nand(nand(X4,nand(X3,nand(X4,X2))),X2),
    inference(transitivity,[status(thm)],[c557,c719]) ).

cnf(c721,plain,
    nand(nand(nand(nand(X,X2),X2),X3),X) = nand(nand(X3,nand(X2,nand(X3,X))),X),
    inference(substitution,[status(thm)],[c720]) ).

cnf(c722,plain,
    nand(nand(nand(nand(nand(X,X2),X2),X3),nand(X,X2)),nand(nand(nand(nand(X,X2),X2),X3),X)) = nand(nand(nand(nand(nand(X,X2),X2),X3),nand(X,X2)),nand(nand(X3,nand(X2,nand(X3,X))),X)),
    inference(congruence,[status(thm)],[c721]) ).

cnf(c723,plain,
    nand(X,X2) = nand(X2,nand(nand(X,X2),X2)),
    inference(symmetry,[status(thm)],[c432]) ).

cnf(c724,plain,
    nand(nand(nand(nand(X,X2),X2),X3),nand(X,X2)) = nand(nand(nand(nand(X,X2),X2),X3),nand(X2,nand(nand(X,X2),X2))),
    inference(congruence,[status(thm)],[c723]) ).

cnf(c725,plain,
    nand(X2,X) = nand(X,X2),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c726,plain,
    nand(nand(X4,X2),nand(nand(X3,X),nand(X4,X3))) = nand(nand(X2,X4),nand(nand(X3,X),nand(X4,X3))),
    inference(congruence,[status(thm)],[c725]) ).

cnf(c727,plain,
    nand(nand(X4,X3),nand(nand(X4,X2),nand(nand(X3,X),nand(X4,X3)))) = nand(nand(X4,X3),nand(nand(X2,X4),nand(nand(X3,X),nand(X4,X3)))),
    inference(congruence,[status(thm)],[c726]) ).

cnf(c728,plain,
    nand(nand(X2,X4),nand(nand(X3,X),nand(X4,X3))) = nand(nand(nand(X3,X),nand(X4,X3)),nand(X2,X4)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c729,plain,
    nand(nand(X4,X3),nand(nand(X2,X4),nand(nand(X3,X),nand(X4,X3)))) = nand(nand(X4,X3),nand(nand(nand(X3,X),nand(X4,X3)),nand(X2,X4))),
    inference(congruence,[status(thm)],[c728]) ).

cnf(c730,plain,
    nand(nand(X2,X),nand(X3,X2)) = nand(nand(X3,X2),nand(X2,X)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c731,plain,
    nand(X3,nand(nand(X2,X),nand(X3,X2))) = nand(X3,nand(nand(X3,X2),nand(X2,X))),
    inference(congruence,[status(thm)],[c730]) ).

cnf(c732,plain,
    nand(X3,nand(nand(X2,X),nand(X3,X2))) = nand(X3,X2),
    inference(transitivity,[status(thm)],[c731,c317]) ).

cnf(c733,plain,
    nand(X3,X2) = nand(X3,nand(nand(X2,X),nand(X3,X2))),
    inference(symmetry,[status(thm)],[c732]) ).

cnf(c734,plain,
    nand(nand(X4,X3),nand(nand(nand(X3,X),nand(X4,X3)),nand(X2,X4))) = nand(nand(X4,nand(nand(X3,X),nand(X4,X3))),nand(nand(nand(X3,X),nand(X4,X3)),nand(X2,X4))),
    inference(congruence,[status(thm)],[c733]) ).

cnf(c735,plain,
    nand(nand(X4,nand(nand(X3,X),nand(X4,X3))),nand(nand(nand(X3,X),nand(X4,X3)),nand(X2,X4))) = nand(nand(X3,X),nand(X4,X3)),
    inference(substitution,[status(thm)],[c281]) ).

cnf(c736,plain,
    nand(nand(X4,X3),nand(nand(nand(X3,X),nand(X4,X3)),nand(X2,X4))) = nand(nand(X3,X),nand(X4,X3)),
    inference(transitivity,[status(thm)],[c734,c735]) ).

cnf(c737,plain,
    nand(nand(X4,X3),nand(nand(X2,X4),nand(nand(X3,X),nand(X4,X3)))) = nand(nand(X3,X),nand(X4,X3)),
    inference(transitivity,[status(thm)],[c729,c736]) ).

cnf(c738,plain,
    nand(nand(X4,X3),nand(nand(X4,X2),nand(nand(X3,X),nand(X4,X3)))) = nand(nand(X3,X),nand(X4,X3)),
    inference(transitivity,[status(thm)],[c727,c737]) ).

cnf(c739,plain,
    nand(nand(X3,nand(nand(X2,X3),X3)),nand(nand(X3,nand(nand(X3,nand(X4,X2)),nand(X,nand(nand(nand(X2,X3),X3),nand(X3,nand(X4,X2)))))),nand(nand(nand(nand(X2,X3),X3),X4),nand(X3,nand(nand(X2,X3),X3))))) = nand(nand(nand(nand(X2,X3),X3),X4),nand(X3,nand(nand(X2,X3),X3))),
    inference(substitution,[status(thm)],[c738]) ).

cnf(c740,plain,
    nand(nand(nand(nand(X2,X3),X3),X4),nand(X3,nand(nand(X2,X3),X3))) = nand(nand(X3,nand(nand(X2,X3),X3)),nand(nand(X3,nand(nand(X3,nand(X4,X2)),nand(X,nand(nand(nand(X2,X3),X3),nand(X3,nand(X4,X2)))))),nand(nand(nand(nand(X2,X3),X3),X4),nand(X3,nand(nand(X2,X3),X3))))),
    inference(symmetry,[status(thm)],[c739]) ).

cnf(c741,plain,
    nand(nand(X4,nand(X3,X2)),nand(X4,nand(X,nand(X2,X4)))) = nand(nand(X4,nand(X,nand(X2,X4))),nand(X4,nand(X3,X2))),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c742,plain,
    nand(nand(X4,nand(X3,nand(X2,X4))),nand(X4,nand(X,X2))) = nand(nand(X4,nand(X,X2)),nand(X4,nand(X3,nand(X2,X4)))),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c743,plain,
    nand(nand(X2,X3),nand(X,X2)) = nand(nand(X2,X3),nand(X2,X)),
    inference(congruence,[status(thm)],[c248]) ).

cnf(c744,plain,
    nand(X3,nand(nand(X2,X3),nand(X,X2))) = nand(X3,nand(nand(X2,X3),nand(X2,X))),
    inference(congruence,[status(thm)],[c743]) ).

cnf(c745,plain,
    nand(X2,X) = nand(X,X2),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c746,plain,
    nand(nand(X2,X3),nand(X2,X)) = nand(nand(X2,X3),nand(X,X2)),
    inference(congruence,[status(thm)],[c745]) ).

cnf(c747,plain,
    nand(X3,nand(nand(X2,X3),nand(X2,X))) = nand(X3,nand(nand(X2,X3),nand(X,X2))),
    inference(congruence,[status(thm)],[c746]) ).

cnf(c748,plain,
    nand(nand(X2,X3),nand(X,X2)) = nand(nand(X,X2),nand(X2,X3)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c749,plain,
    nand(X3,nand(nand(X2,X3),nand(X,X2))) = nand(X3,nand(nand(X,X2),nand(X2,X3))),
    inference(congruence,[status(thm)],[c748]) ).

cnf(c750,plain,
    nand(X3,nand(nand(X,X2),nand(X2,X3))) = nand(nand(nand(X,X2),nand(X2,X3)),X3),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c751,plain,
    nand(nand(X2,X3),nand(X3,nand(X,X2))) = X3,
    inference(substitution,[status(thm)],[c281]) ).

cnf(c752,plain,
    X3 = nand(nand(X2,X3),nand(X3,nand(X,X2))),
    inference(symmetry,[status(thm)],[c751]) ).

cnf(c753,plain,
    nand(nand(nand(X,X2),nand(X2,X3)),X3) = nand(nand(nand(X,X2),nand(X2,X3)),nand(nand(X2,X3),nand(X3,nand(X,X2)))),
    inference(congruence,[status(thm)],[c752]) ).

cnf(c754,plain,
    nand(nand(nand(X,X2),nand(X2,X3)),nand(nand(X2,X3),nand(X3,nand(X,X2)))) = nand(X2,X3),
    inference(substitution,[status(thm)],[c281]) ).

cnf(c755,plain,
    nand(nand(nand(X,X2),nand(X2,X3)),X3) = nand(X2,X3),
    inference(transitivity,[status(thm)],[c753,c754]) ).

cnf(c756,plain,
    nand(X3,nand(nand(X,X2),nand(X2,X3))) = nand(X2,X3),
    inference(transitivity,[status(thm)],[c750,c755]) ).

cnf(c757,plain,
    nand(X3,nand(nand(X2,X3),nand(X,X2))) = nand(X2,X3),
    inference(transitivity,[status(thm)],[c749,c756]) ).

cnf(c758,plain,
    nand(X3,nand(nand(X2,X3),nand(X2,X))) = nand(X2,X3),
    inference(transitivity,[status(thm)],[c747,c757]) ).

cnf(c759,plain,
    nand(X3,nand(nand(X2,X3),nand(X,X2))) = nand(X2,X3),
    inference(transitivity,[status(thm)],[c744,c758]) ).

cnf(c760,plain,
    nand(X2,X3) = nand(X3,nand(nand(X2,X3),nand(X,X2))),
    inference(symmetry,[status(thm)],[c759]) ).

cnf(c761,plain,
    nand(X3,nand(X2,X4)) = nand(X3,nand(X4,nand(nand(X2,X4),nand(X,X2)))),
    inference(congruence,[status(thm)],[c760]) ).

cnf(c762,plain,
    nand(X4,nand(X3,nand(X2,X4))) = nand(X4,nand(X3,nand(X4,nand(nand(X2,X4),nand(X,X2))))),
    inference(congruence,[status(thm)],[c761]) ).

cnf(c763,plain,
    nand(nand(X4,nand(X,X2)),nand(X4,nand(X3,nand(X2,X4)))) = nand(nand(X4,nand(X,X2)),nand(X4,nand(X3,nand(X4,nand(nand(X2,X4),nand(X,X2)))))),
    inference(congruence,[status(thm)],[c762]) ).

cnf(c764,plain,
    nand(X2,nand(X4,nand(X,X3))) = nand(nand(X4,nand(X,X3)),X2),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c765,plain,
    nand(X4,nand(X2,nand(X4,nand(X,X3)))) = nand(X4,nand(nand(X4,nand(X,X3)),X2)),
    inference(congruence,[status(thm)],[c764]) ).

cnf(c766,plain,
    nand(nand(X4,X3),nand(X4,nand(X2,nand(X4,nand(X,X3))))) = nand(nand(X4,X3),nand(X4,nand(nand(X4,nand(X,X3)),X2))),
    inference(congruence,[status(thm)],[c765]) ).

cnf(c767,plain,
    nand(X2,X) = nand(X,X2),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c768,plain,
    nand(nand(X4,X3),nand(X4,nand(nand(X4,nand(X,X3)),X2))) = nand(nand(X3,X4),nand(X4,nand(nand(X4,nand(X,X3)),X2))),
    inference(congruence,[status(thm)],[c767]) ).

cnf(c769,plain,
    nand(nand(X2,X3),nand(X3,nand(X,X2))) = X3,
    inference(substitution,[status(thm)],[c281]) ).

cnf(c770,plain,
    X3 = nand(nand(X2,X3),nand(X3,nand(X,X2))),
    inference(symmetry,[status(thm)],[c769]) ).

cnf(c771,plain,
    nand(X4,nand(nand(X4,nand(X,X3)),X2)) = nand(nand(nand(X3,X4),nand(X4,nand(X,X3))),nand(nand(X4,nand(X,X3)),X2)),
    inference(congruence,[status(thm)],[c770]) ).

cnf(c772,plain,
    nand(nand(X3,X4),nand(X4,nand(nand(X4,nand(X,X3)),X2))) = nand(nand(X3,X4),nand(nand(nand(X3,X4),nand(X4,nand(X,X3))),nand(nand(X4,nand(X,X3)),X2))),
    inference(congruence,[status(thm)],[c771]) ).

cnf(c773,plain,
    nand(nand(X3,X4),nand(nand(nand(X3,X4),nand(X4,nand(X,X3))),nand(nand(X4,nand(X,X3)),X2))) = nand(nand(X3,X4),nand(X4,nand(X,X3))),
    inference(substitution,[status(thm)],[c317]) ).

cnf(c774,plain,
    nand(nand(X2,X3),nand(X3,nand(X,X2))) = X3,
    inference(substitution,[status(thm)],[c281]) ).

cnf(c775,plain,
    nand(nand(X3,X4),nand(nand(nand(X3,X4),nand(X4,nand(X,X3))),nand(nand(X4,nand(X,X3)),X2))) = X4,
    inference(transitivity,[status(thm)],[c773,c774]) ).

cnf(c776,plain,
    nand(nand(X3,X4),nand(X4,nand(nand(X4,nand(X,X3)),X2))) = X4,
    inference(transitivity,[status(thm)],[c772,c775]) ).

cnf(c777,plain,
    nand(nand(X4,X3),nand(X4,nand(nand(X4,nand(X,X3)),X2))) = X4,
    inference(transitivity,[status(thm)],[c768,c776]) ).

cnf(c778,plain,
    nand(nand(X4,X3),nand(X4,nand(X2,nand(X4,nand(X,X3))))) = X4,
    inference(transitivity,[status(thm)],[c766,c777]) ).

cnf(c779,plain,
    nand(nand(X4,nand(X,X2)),nand(X4,nand(X3,nand(X4,nand(nand(X2,X4),nand(X,X2)))))) = X4,
    inference(substitution,[status(thm)],[c778]) ).

cnf(c780,plain,
    nand(nand(X4,nand(X,X2)),nand(X4,nand(X3,nand(X2,X4)))) = X4,
    inference(transitivity,[status(thm)],[c763,c779]) ).

cnf(c781,plain,
    nand(nand(X4,nand(X3,nand(X2,X4))),nand(X4,nand(X,X2))) = X4,
    inference(transitivity,[status(thm)],[c742,c780]) ).

cnf(c782,plain,
    nand(nand(X4,nand(X,nand(X2,X4))),nand(X4,nand(X3,X2))) = X4,
    inference(substitution,[status(thm)],[c781]) ).

cnf(c783,plain,
    nand(nand(X4,nand(X3,X2)),nand(X4,nand(X,nand(X2,X4)))) = X4,
    inference(transitivity,[status(thm)],[c741,c782]) ).

cnf(c784,plain,
    X4 = nand(nand(X4,nand(X3,X2)),nand(X4,nand(X,nand(X2,X4)))),
    inference(symmetry,[status(thm)],[c783]) ).

cnf(c785,plain,
    nand(X5,nand(nand(X5,nand(X4,X3)),nand(X2,nand(nand(nand(X3,X5),X5),nand(X5,nand(X4,X3)))))) = nand(nand(nand(X5,nand(X4,X3)),nand(X5,nand(X,nand(X3,X5)))),nand(nand(X5,nand(X4,X3)),nand(X2,nand(nand(nand(X3,X5),X5),nand(X5,nand(X4,X3)))))),
    inference(congruence,[status(thm)],[c784]) ).

cnf(c786,plain,
    nand(X3,nand(X3,nand(X,nand(X2,X3)))) = nand(nand(X3,nand(X,nand(X2,X3))),X3),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c787,plain,
    nand(nand(X4,nand(X3,X2)),nand(X4,nand(X4,nand(X,nand(X2,X4))))) = nand(nand(X4,nand(X3,X2)),nand(nand(X4,nand(X,nand(X2,X4))),X4)),
    inference(congruence,[status(thm)],[c786]) ).

cnf(c788,plain,
    X4 = nand(nand(X4,nand(X3,X2)),nand(X4,nand(X,nand(X2,X4)))),
    inference(symmetry,[status(thm)],[c783]) ).

cnf(c789,plain,
    nand(nand(X4,nand(X,nand(X2,X4))),X4) = nand(nand(X4,nand(X,nand(X2,X4))),nand(nand(X4,nand(X3,X2)),nand(X4,nand(X,nand(X2,X4))))),
    inference(congruence,[status(thm)],[c788]) ).

cnf(c790,plain,
    nand(nand(X4,nand(X3,X2)),nand(nand(X4,nand(X,nand(X2,X4))),X4)) = nand(nand(X4,nand(X3,X2)),nand(nand(X4,nand(X,nand(X2,X4))),nand(nand(X4,nand(X3,X2)),nand(X4,nand(X,nand(X2,X4)))))),
    inference(congruence,[status(thm)],[c789]) ).

cnf(c791,plain,
    nand(nand(X4,nand(X3,X2)),nand(nand(X4,nand(X,nand(X2,X4))),nand(nand(X4,nand(X3,X2)),nand(X4,nand(X,nand(X2,X4)))))) = nand(nand(X4,nand(X3,X2)),nand(X4,nand(X3,X2))),
    inference(substitution,[status(thm)],[c332]) ).

cnf(c792,plain,
    nand(nand(nand(X,X3),X3),nand(X3,nand(X2,X))) = nand(nand(X3,nand(X2,X)),nand(nand(X,X3),X3)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c793,plain,
    nand(nand(X3,nand(X2,X)),nand(X,X3)) = nand(nand(X3,nand(X2,X)),nand(X3,X)),
    inference(congruence,[status(thm)],[c248]) ).

cnf(c794,plain,
    nand(nand(X,X),nand(X2,X)) = X,
    inference(substitution,[status(thm)],[c375]) ).

cnf(c795,plain,
    X = nand(nand(X,X),nand(X2,X)),
    inference(symmetry,[status(thm)],[c794]) ).

cnf(c796,plain,
    nand(X3,X) = nand(X3,nand(nand(X,X),nand(X2,X))),
    inference(congruence,[status(thm)],[c795]) ).

cnf(c797,plain,
    nand(nand(X3,nand(X2,X)),nand(X3,X)) = nand(nand(X3,nand(X2,X)),nand(X3,nand(nand(X,X),nand(X2,X)))),
    inference(congruence,[status(thm)],[c796]) ).

cnf(c798,plain,
    nand(nand(X3,nand(X2,X)),nand(X3,nand(nand(X,X),nand(X2,X)))) = X3,
    inference(substitution,[status(thm)],[c524]) ).

cnf(c799,plain,
    nand(nand(X3,nand(X2,X)),nand(X3,X)) = X3,
    inference(transitivity,[status(thm)],[c797,c798]) ).

cnf(c800,plain,
    nand(nand(X3,nand(X2,X)),nand(X,X3)) = X3,
    inference(transitivity,[status(thm)],[c793,c799]) ).

cnf(c801,plain,
    X3 = nand(nand(X3,nand(X2,X)),nand(X,X3)),
    inference(symmetry,[status(thm)],[c800]) ).

cnf(c802,plain,
    nand(nand(X,X3),X3) = nand(nand(X,X3),nand(nand(X3,nand(X2,X)),nand(X,X3))),
    inference(congruence,[status(thm)],[c801]) ).

cnf(c803,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(X,X3),X3)) = nand(nand(X3,nand(X2,X)),nand(nand(X,X3),nand(nand(X3,nand(X2,X)),nand(X,X3)))),
    inference(congruence,[status(thm)],[c802]) ).

cnf(c804,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(X,X3),nand(nand(X3,nand(X2,X)),nand(X,X3)))) = nand(nand(X3,nand(X2,X)),nand(X3,nand(X2,X))),
    inference(substitution,[status(thm)],[c332]) ).

cnf(c805,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(X,X3),X3)) = nand(nand(X3,nand(X2,X)),nand(X3,nand(X2,X))),
    inference(transitivity,[status(thm)],[c803,c804]) ).

cnf(c806,plain,
    nand(nand(nand(X,X3),X3),nand(X3,nand(X2,X))) = nand(nand(X3,nand(X2,X)),nand(X3,nand(X2,X))),
    inference(transitivity,[status(thm)],[c792,c805]) ).

cnf(c807,plain,
    nand(nand(X3,nand(X2,X)),nand(X3,nand(X2,X))) = nand(nand(nand(X,X3),X3),nand(X3,nand(X2,X))),
    inference(symmetry,[status(thm)],[c806]) ).

cnf(c808,plain,
    nand(nand(X4,nand(X3,X2)),nand(nand(X4,nand(X,nand(X2,X4))),nand(nand(X4,nand(X3,X2)),nand(X4,nand(X,nand(X2,X4)))))) = nand(nand(nand(X2,X4),X4),nand(X4,nand(X3,X2))),
    inference(transitivity,[status(thm)],[c791,c807]) ).

cnf(c809,plain,
    nand(nand(X4,nand(X3,X2)),nand(nand(X4,nand(X,nand(X2,X4))),X4)) = nand(nand(nand(X2,X4),X4),nand(X4,nand(X3,X2))),
    inference(transitivity,[status(thm)],[c790,c808]) ).

cnf(c810,plain,
    nand(nand(X4,nand(X3,X2)),nand(X4,nand(X4,nand(X,nand(X2,X4))))) = nand(nand(nand(X2,X4),X4),nand(X4,nand(X3,X2))),
    inference(transitivity,[status(thm)],[c787,c809]) ).

cnf(c811,plain,
    nand(nand(nand(X2,X4),X4),nand(X4,nand(X3,X2))) = nand(nand(X4,nand(X3,X2)),nand(X4,nand(X4,nand(X,nand(X2,X4))))),
    inference(symmetry,[status(thm)],[c810]) ).

cnf(c812,plain,
    nand(X2,nand(nand(nand(X3,X5),X5),nand(X5,nand(X4,X3)))) = nand(X2,nand(nand(X5,nand(X4,X3)),nand(X5,nand(X5,nand(X,nand(X3,X5)))))),
    inference(congruence,[status(thm)],[c811]) ).

cnf(c813,plain,
    nand(nand(X5,nand(X4,X3)),nand(X2,nand(nand(nand(X3,X5),X5),nand(X5,nand(X4,X3))))) = nand(nand(X5,nand(X4,X3)),nand(X2,nand(nand(X5,nand(X4,X3)),nand(X5,nand(X5,nand(X,nand(X3,X5))))))),
    inference(congruence,[status(thm)],[c812]) ).

cnf(c814,plain,
    nand(nand(nand(X5,nand(X4,X3)),nand(X5,nand(X,nand(X3,X5)))),nand(nand(X5,nand(X4,X3)),nand(X2,nand(nand(nand(X3,X5),X5),nand(X5,nand(X4,X3)))))) = nand(nand(nand(X5,nand(X4,X3)),nand(X5,nand(X,nand(X3,X5)))),nand(nand(X5,nand(X4,X3)),nand(X2,nand(nand(X5,nand(X4,X3)),nand(X5,nand(X5,nand(X,nand(X3,X5)))))))),
    inference(congruence,[status(thm)],[c813]) ).

cnf(c815,plain,
    nand(nand(nand(X5,nand(X4,X3)),nand(X5,nand(X,nand(X3,X5)))),nand(nand(X5,nand(X4,X3)),nand(X2,nand(nand(X5,nand(X4,X3)),nand(X5,nand(X5,nand(X,nand(X3,X5)))))))) = nand(X5,nand(X4,X3)),
    inference(substitution,[status(thm)],[c778]) ).

cnf(c816,plain,
    nand(nand(nand(X5,nand(X4,X3)),nand(X5,nand(X,nand(X3,X5)))),nand(nand(X5,nand(X4,X3)),nand(X2,nand(nand(nand(X3,X5),X5),nand(X5,nand(X4,X3)))))) = nand(X5,nand(X4,X3)),
    inference(transitivity,[status(thm)],[c814,c815]) ).

cnf(c817,plain,
    nand(X4,nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(nand(X2,X4),X4),nand(X4,nand(X3,X2)))))) = nand(X4,nand(X3,X2)),
    inference(transitivity,[status(thm)],[c785,c816]) ).

cnf(c818,plain,
    nand(X3,nand(nand(X3,nand(X4,X2)),nand(X,nand(nand(nand(X2,X3),X3),nand(X3,nand(X4,X2)))))) = nand(X3,nand(X4,X2)),
    inference(substitution,[status(thm)],[c817]) ).

cnf(c819,plain,
    nand(nand(X3,nand(nand(X3,nand(X4,X2)),nand(X,nand(nand(nand(X2,X3),X3),nand(X3,nand(X4,X2)))))),nand(nand(nand(nand(X2,X3),X3),X4),nand(X3,nand(nand(X2,X3),X3)))) = nand(nand(X3,nand(X4,X2)),nand(nand(nand(nand(X2,X3),X3),X4),nand(X3,nand(nand(X2,X3),X3)))),
    inference(congruence,[status(thm)],[c818]) ).

cnf(c820,plain,
    nand(nand(X3,nand(nand(X2,X3),X3)),nand(nand(X3,nand(nand(X3,nand(X4,X2)),nand(X,nand(nand(nand(X2,X3),X3),nand(X3,nand(X4,X2)))))),nand(nand(nand(nand(X2,X3),X3),X4),nand(X3,nand(nand(X2,X3),X3))))) = nand(nand(X3,nand(nand(X2,X3),X3)),nand(nand(X3,nand(X4,X2)),nand(nand(nand(nand(X2,X3),X3),X4),nand(X3,nand(nand(X2,X3),X3))))),
    inference(congruence,[status(thm)],[c819]) ).

cnf(c821,plain,
    nand(nand(nand(nand(X,X2),X2),X3),nand(X2,nand(nand(X,X2),X2))) = nand(nand(nand(nand(X,X2),X2),X3),nand(X,X2)),
    inference(congruence,[status(thm)],[c432]) ).

cnf(c822,plain,
    nand(nand(X2,nand(X3,X)),nand(nand(nand(nand(X,X2),X2),X3),nand(X2,nand(nand(X,X2),X2)))) = nand(nand(X2,nand(X3,X)),nand(nand(nand(nand(X,X2),X2),X3),nand(X,X2))),
    inference(congruence,[status(thm)],[c821]) ).

cnf(c823,plain,
    nand(nand(X2,nand(nand(X,X2),X2)),nand(nand(X2,nand(X3,X)),nand(nand(nand(nand(X,X2),X2),X3),nand(X2,nand(nand(X,X2),X2))))) = nand(nand(X2,nand(nand(X,X2),X2)),nand(nand(X2,nand(X3,X)),nand(nand(nand(nand(X,X2),X2),X3),nand(X,X2)))),
    inference(congruence,[status(thm)],[c822]) ).

cnf(c824,plain,
    nand(nand(X2,nand(nand(X,X2),X2)),nand(nand(X2,nand(X3,X)),nand(nand(nand(nand(X,X2),X2),X3),nand(X,X2)))) = nand(nand(X,X2),nand(nand(X2,nand(X3,X)),nand(nand(nand(nand(X,X2),X2),X3),nand(X,X2)))),
    inference(congruence,[status(thm)],[c432]) ).

cnf(c825,plain,
    X3 = nand(nand(X3,X2),nand(X3,nand(X2,nand(X,X4)))),
    inference(symmetry,[status(thm)],[c514]) ).

cnf(c826,plain,
    nand(X4,nand(nand(X4,X3),X5)) = nand(nand(nand(X4,X3),nand(X4,nand(X3,nand(X2,X)))),nand(nand(X4,X3),X5)),
    inference(congruence,[status(thm)],[c825]) ).

cnf(c827,plain,
    nand(nand(nand(X6,X5),nand(nand(X4,X3),X6)),nand(X4,nand(nand(X4,X3),X6))) = nand(nand(nand(X6,X5),nand(nand(X4,X3),X6)),nand(nand(nand(X4,X3),nand(X4,nand(X3,nand(X2,X)))),nand(nand(X4,X3),X6))),
    inference(congruence,[status(thm)],[c826]) ).

cnf(c828,plain,
    nand(nand(X2,X),nand(X2,X3)) = nand(nand(X2,X3),nand(X2,X)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c829,plain,
    nand(nand(nand(X4,X3),nand(X2,X4)),nand(nand(X2,X),nand(X2,X4))) = nand(nand(nand(X4,X3),nand(X2,X4)),nand(nand(X2,X4),nand(X2,X))),
    inference(congruence,[status(thm)],[c828]) ).

cnf(c830,plain,
    nand(X,nand(nand(X3,X2),nand(X,X3))) = nand(X,X3),
    inference(substitution,[status(thm)],[c732]) ).

cnf(c831,plain,
    nand(X,X3) = nand(X,nand(nand(X3,X2),nand(X,X3))),
    inference(symmetry,[status(thm)],[c830]) ).

cnf(c832,plain,
    nand(nand(X2,X4),nand(X2,X)) = nand(nand(X2,nand(nand(X4,X3),nand(X2,X4))),nand(X2,X)),
    inference(congruence,[status(thm)],[c831]) ).

cnf(c833,plain,
    nand(nand(nand(X4,X3),nand(X2,X4)),nand(nand(X2,X4),nand(X2,X))) = nand(nand(nand(X4,X3),nand(X2,X4)),nand(nand(X2,nand(nand(X4,X3),nand(X2,X4))),nand(X2,X))),
    inference(congruence,[status(thm)],[c832]) ).

cnf(c834,plain,
    nand(nand(nand(X4,X3),nand(X2,X4)),nand(nand(X2,nand(nand(X4,X3),nand(X2,X4))),nand(X2,X))) = nand(X2,nand(nand(X4,X3),nand(X2,X4))),
    inference(substitution,[status(thm)],[c758]) ).

cnf(c835,plain,
    nand(X,nand(nand(X3,X2),nand(X,X3))) = nand(X,X3),
    inference(substitution,[status(thm)],[c732]) ).

cnf(c836,plain,
    nand(nand(nand(X4,X3),nand(X2,X4)),nand(nand(X2,nand(nand(X4,X3),nand(X2,X4))),nand(X2,X))) = nand(X2,X4),
    inference(transitivity,[status(thm)],[c834,c835]) ).

cnf(c837,plain,
    nand(nand(nand(X4,X3),nand(X2,X4)),nand(nand(X2,X4),nand(X2,X))) = nand(X2,X4),
    inference(transitivity,[status(thm)],[c833,c836]) ).

cnf(c838,plain,
    nand(nand(nand(X4,X3),nand(X2,X4)),nand(nand(X2,X),nand(X2,X4))) = nand(X2,X4),
    inference(transitivity,[status(thm)],[c829,c837]) ).

cnf(c839,plain,
    nand(nand(nand(X6,X5),nand(nand(X4,X3),X6)),nand(nand(nand(X4,X3),nand(X4,nand(X3,nand(X2,X)))),nand(nand(X4,X3),X6))) = nand(nand(X4,X3),X6),
    inference(substitution,[status(thm)],[c838]) ).

cnf(c840,plain,
    nand(nand(nand(X4,X3),nand(nand(X2,X),X4)),nand(X2,nand(nand(X2,X),X4))) = nand(nand(X2,X),X4),
    inference(transitivity,[status(thm)],[c827,c839]) ).

cnf(c841,plain,
    nand(nand(nand(nand(X,X3),X3),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3))),nand(nand(nand(X,X3),X3),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3)))) = nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3)),
    inference(substitution,[status(thm)],[c840]) ).

cnf(c842,plain,
    nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3)) = nand(nand(nand(nand(X,X3),X3),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3))),nand(nand(nand(X,X3),X3),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3)))),
    inference(symmetry,[status(thm)],[c841]) ).

cnf(c843,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3))) = nand(nand(X3,nand(X2,X)),nand(nand(nand(nand(X,X3),X3),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3))),nand(nand(nand(X,X3),X3),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3))))),
    inference(congruence,[status(thm)],[c842]) ).

cnf(c844,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(nand(nand(X,X3),X3),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3))),nand(nand(nand(X,X3),X3),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3))))) = nand(nand(X3,nand(X2,X)),nand(nand(X3,nand(X2,X)),nand(nand(nand(X,X3),X3),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3))))),
    inference(substitution,[status(thm)],[c341]) ).

cnf(c845,plain,
    nand(nand(nand(nand(nand(X3,X2),X2),X),nand(X2,nand(X,X3))),nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2))) = nand(nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2)),nand(nand(nand(nand(X3,X2),X2),X),nand(X2,nand(X,X3)))),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c846,plain,
    nand(nand(nand(nand(X4,X3),X3),X2),nand(X,X)) = nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(nand(X4,X3),X3),X2),X)),
    inference(substitution,[status(thm)],[c341]) ).

cnf(c847,plain,
    nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(nand(X4,X3),X3),X2),X)) = nand(nand(nand(nand(X4,X3),X3),X2),nand(X,X)),
    inference(symmetry,[status(thm)],[c846]) ).

cnf(c848,plain,
    nand(nand(nand(nand(X4,X3),X3),X2),nand(X,nand(nand(nand(nand(X4,X3),X3),X2),nand(X,nand(X2,X4))))) = nand(nand(nand(nand(X4,X3),X3),X2),nand(X,nand(X2,X4))),
    inference(substitution,[status(thm)],[c325]) ).

cnf(c849,plain,
    nand(nand(nand(nand(X4,X3),X3),X2),nand(X,nand(X2,X4))) = nand(nand(nand(nand(X4,X3),X3),X2),nand(X,nand(nand(nand(nand(X4,X3),X3),X2),nand(X,nand(X2,X4))))),
    inference(symmetry,[status(thm)],[c848]) ).

cnf(c850,plain,
    nand(nand(nand(nand(X3,X2),X2),X),nand(X4,nand(X,X3))) = nand(nand(X4,nand(X,X3)),nand(nand(nand(X3,X2),X2),X)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c851,plain,
    nand(X4,nand(nand(nand(nand(X3,X2),X2),X),nand(X4,nand(X,X3)))) = nand(X4,nand(nand(X4,nand(X,X3)),nand(nand(nand(X3,X2),X2),X))),
    inference(congruence,[status(thm)],[c850]) ).

cnf(c852,plain,
    nand(X2,nand(X2,nand(X,X))) = nand(X2,nand(X2,nand(X2,X))),
    inference(congruence,[status(thm)],[c341]) ).

cnf(c853,plain,
    nand(X2,nand(nand(X2,X),nand(X2,X))) = nand(X2,nand(X2,nand(X2,X))),
    inference(substitution,[status(thm)],[c341]) ).

cnf(c854,plain,
    nand(X2,nand(X2,nand(X2,X))) = nand(X2,nand(nand(X2,X),nand(X2,X))),
    inference(symmetry,[status(thm)],[c853]) ).

cnf(c855,plain,
    nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X)))) = X2,
    inference(substitution,[status(thm)],[c198]) ).

cnf(c856,plain,
    X2 = nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X)))),
    inference(symmetry,[status(thm)],[c855]) ).

cnf(c857,plain,
    nand(X2,nand(nand(X2,X),nand(X2,X))) = nand(nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X)))),nand(nand(X2,X),nand(X2,X))),
    inference(congruence,[status(thm)],[c856]) ).

cnf(c858,plain,
    X2 = nand(nand(X2,X),nand(X2,nand(X2,X))),
    inference(symmetry,[status(thm)],[c198]) ).

cnf(c859,plain,
    nand(X2,nand(X2,nand(X2,X))) = nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X))),
    inference(congruence,[status(thm)],[c858]) ).

cnf(c860,plain,
    nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X)))) = nand(nand(X2,nand(X2,X)),nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X)))),
    inference(congruence,[status(thm)],[c859]) ).

cnf(c861,plain,
    nand(nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X)))),nand(nand(X2,X),nand(X2,X))) = nand(nand(nand(X2,nand(X2,X)),nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X)))),nand(nand(X2,X),nand(X2,X))),
    inference(congruence,[status(thm)],[c860]) ).

cnf(c862,plain,
    nand(nand(nand(X2,nand(X2,X)),nand(nand(nand(X2,X),nand(X2,nand(X2,X))),nand(X2,nand(X2,X)))),nand(nand(X2,X),nand(X2,X))) = nand(X2,X),
    inference(substitution,[status(thm)],[c95]) ).

cnf(c863,plain,
    nand(nand(nand(X2,nand(X2,X)),nand(X2,nand(X2,nand(X2,X)))),nand(nand(X2,X),nand(X2,X))) = nand(X2,X),
    inference(transitivity,[status(thm)],[c861,c862]) ).

cnf(c864,plain,
    nand(X2,nand(nand(X2,X),nand(X2,X))) = nand(X2,X),
    inference(transitivity,[status(thm)],[c857,c863]) ).

cnf(c865,plain,
    nand(X2,nand(X2,nand(X2,X))) = nand(X2,X),
    inference(transitivity,[status(thm)],[c854,c864]) ).

cnf(c866,plain,
    nand(X2,nand(X2,nand(X,X))) = nand(X2,X),
    inference(transitivity,[status(thm)],[c852,c865]) ).

cnf(c867,plain,
    nand(nand(X4,nand(X,X3)),nand(nand(X4,nand(X,X3)),nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X3,X2),X2),X)))) = nand(nand(X4,nand(X,X3)),nand(nand(nand(X3,X2),X2),X)),
    inference(substitution,[status(thm)],[c866]) ).

cnf(c868,plain,
    nand(nand(X4,nand(X,X3)),nand(nand(nand(X3,X2),X2),X)) = nand(nand(X4,nand(X,X3)),nand(nand(X4,nand(X,X3)),nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X3,X2),X2),X)))),
    inference(symmetry,[status(thm)],[c867]) ).

cnf(c869,plain,
    nand(X4,nand(nand(X4,nand(X,X3)),nand(nand(nand(X3,X2),X2),X))) = nand(X4,nand(nand(X4,nand(X,X3)),nand(nand(X4,nand(X,X3)),nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X3,X2),X2),X))))),
    inference(congruence,[status(thm)],[c868]) ).

cnf(c870,plain,
    nand(nand(X4,X3),nand(nand(X2,X3),nand(nand(nand(nand(X3,X),X),X4),nand(nand(nand(X3,X),X),X4)))) = nand(nand(nand(X2,X3),nand(nand(nand(nand(X3,X),X),X4),nand(nand(nand(X3,X),X),X4))),nand(X4,X3)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c871,plain,
    nand(nand(nand(nand(nand(X3,X),X),X4),nand(nand(nand(X3,X),X),X4)),nand(nand(X4,X3),nand(X2,X3))) = nand(X4,X3),
    inference(substitution,[status(thm)],[c546]) ).

cnf(c872,plain,
    nand(X4,X3) = nand(nand(nand(nand(nand(X3,X),X),X4),nand(nand(nand(X3,X),X),X4)),nand(nand(X4,X3),nand(X2,X3))),
    inference(symmetry,[status(thm)],[c871]) ).

cnf(c873,plain,
    nand(nand(nand(X2,X3),nand(nand(nand(nand(X3,X),X),X4),nand(nand(nand(X3,X),X),X4))),nand(X4,X3)) = nand(nand(nand(X2,X3),nand(nand(nand(nand(X3,X),X),X4),nand(nand(nand(X3,X),X),X4))),nand(nand(nand(nand(nand(X3,X),X),X4),nand(nand(nand(X3,X),X),X4)),nand(nand(X4,X3),nand(X2,X3)))),
    inference(congruence,[status(thm)],[c872]) ).

cnf(c874,plain,
    nand(nand(nand(X2,X3),nand(nand(nand(nand(X3,X),X),X4),nand(nand(nand(X3,X),X),X4))),nand(nand(nand(nand(nand(X3,X),X),X4),nand(nand(nand(X3,X),X),X4)),nand(nand(X4,X3),nand(X2,X3)))) = nand(nand(nand(nand(X3,X),X),X4),nand(nand(nand(X3,X),X),X4)),
    inference(substitution,[status(thm)],[c281]) ).

cnf(c875,plain,
    nand(nand(nand(X2,X3),nand(nand(nand(nand(X3,X),X),X4),nand(nand(nand(X3,X),X),X4))),nand(X4,X3)) = nand(nand(nand(nand(X3,X),X),X4),nand(nand(nand(X3,X),X),X4)),
    inference(transitivity,[status(thm)],[c873,c874]) ).

cnf(c876,plain,
    nand(nand(X4,X3),nand(nand(X2,X3),nand(nand(nand(nand(X3,X),X),X4),nand(nand(nand(X3,X),X),X4)))) = nand(nand(nand(nand(X3,X),X),X4),nand(nand(nand(X3,X),X),X4)),
    inference(transitivity,[status(thm)],[c870,c875]) ).

cnf(c877,plain,
    nand(nand(X2,X4),nand(nand(X,X4),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2)))) = nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2)),
    inference(substitution,[status(thm)],[c876]) ).

cnf(c878,plain,
    nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2)) = nand(nand(X2,X4),nand(nand(X,X4),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2)))),
    inference(symmetry,[status(thm)],[c877]) ).

cnf(c879,plain,
    nand(nand(X5,nand(X2,X4)),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2))) = nand(nand(X5,nand(X2,X4)),nand(nand(X2,X4),nand(nand(X,X4),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2))))),
    inference(congruence,[status(thm)],[c878]) ).

cnf(c880,plain,
    nand(nand(X5,nand(X2,X4)),nand(nand(X5,nand(X2,X4)),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2)))) = nand(nand(X5,nand(X2,X4)),nand(nand(X5,nand(X2,X4)),nand(nand(X2,X4),nand(nand(X,X4),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2)))))),
    inference(congruence,[status(thm)],[c879]) ).

cnf(c881,plain,
    nand(X5,nand(nand(X5,nand(X2,X4)),nand(nand(X5,nand(X2,X4)),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2))))) = nand(X5,nand(nand(X5,nand(X2,X4)),nand(nand(X5,nand(X2,X4)),nand(nand(X2,X4),nand(nand(X,X4),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2))))))),
    inference(congruence,[status(thm)],[c880]) ).

cnf(c882,plain,
    nand(nand(X3,X2),nand(nand(X3,X2),nand(X2,X))) = nand(nand(nand(X3,X2),nand(X2,X)),nand(X3,X2)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c883,plain,
    nand(X3,nand(nand(X3,X2),nand(nand(X3,X2),nand(X2,X)))) = nand(X3,nand(nand(nand(X3,X2),nand(X2,X)),nand(X3,X2))),
    inference(congruence,[status(thm)],[c882]) ).

cnf(c884,plain,
    nand(X3,X2) = nand(X3,nand(nand(X3,X2),nand(X2,X))),
    inference(symmetry,[status(thm)],[c317]) ).

cnf(c885,plain,
    nand(nand(nand(X3,X2),nand(X2,X)),nand(X3,X2)) = nand(nand(nand(X3,X2),nand(X2,X)),nand(X3,nand(nand(X3,X2),nand(X2,X)))),
    inference(congruence,[status(thm)],[c884]) ).

cnf(c886,plain,
    nand(X3,nand(nand(nand(X3,X2),nand(X2,X)),nand(X3,X2))) = nand(X3,nand(nand(nand(X3,X2),nand(X2,X)),nand(X3,nand(nand(X3,X2),nand(X2,X))))),
    inference(congruence,[status(thm)],[c885]) ).

cnf(c887,plain,
    nand(X3,nand(nand(nand(X3,X2),nand(X2,X)),nand(X3,nand(nand(X3,X2),nand(X2,X))))) = nand(X3,X3),
    inference(substitution,[status(thm)],[c332]) ).

cnf(c888,plain,
    nand(X3,nand(nand(nand(X3,X2),nand(X2,X)),nand(X3,X2))) = nand(X3,X3),
    inference(transitivity,[status(thm)],[c886,c887]) ).

cnf(c889,plain,
    nand(X3,nand(nand(X3,X2),nand(nand(X3,X2),nand(X2,X)))) = nand(X3,X3),
    inference(transitivity,[status(thm)],[c883,c888]) ).

cnf(c890,plain,
    nand(X5,nand(nand(X5,nand(X2,X4)),nand(nand(X5,nand(X2,X4)),nand(nand(X2,X4),nand(nand(X,X4),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2))))))) = nand(X5,X5),
    inference(substitution,[status(thm)],[c889]) ).

cnf(c891,plain,
    nand(X4,nand(nand(X4,nand(X,X3)),nand(nand(X4,nand(X,X3)),nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X3,X2),X2),X))))) = nand(X4,X4),
    inference(transitivity,[status(thm)],[c881,c890]) ).

cnf(c892,plain,
    nand(X4,nand(nand(X4,nand(X,X3)),nand(nand(nand(X3,X2),X2),X))) = nand(X4,X4),
    inference(transitivity,[status(thm)],[c869,c891]) ).

cnf(c893,plain,
    nand(X4,nand(nand(nand(nand(X3,X2),X2),X),nand(X4,nand(X,X3)))) = nand(X4,X4),
    inference(transitivity,[status(thm)],[c851,c892]) ).

cnf(c894,plain,
    nand(X,nand(nand(nand(nand(X4,X3),X3),X2),nand(X,nand(X2,X4)))) = nand(X,X),
    inference(substitution,[status(thm)],[c893]) ).

cnf(c895,plain,
    nand(nand(nand(nand(X4,X3),X3),X2),nand(X,nand(nand(nand(nand(X4,X3),X3),X2),nand(X,nand(X2,X4))))) = nand(nand(nand(nand(X4,X3),X3),X2),nand(X,X)),
    inference(congruence,[status(thm)],[c894]) ).

cnf(c896,plain,
    nand(nand(nand(nand(X4,X3),X3),X2),nand(X,nand(X2,X4))) = nand(nand(nand(nand(X4,X3),X3),X2),nand(X,X)),
    inference(transitivity,[status(thm)],[c849,c895]) ).

cnf(c897,plain,
    nand(nand(nand(nand(X4,X3),X3),X2),nand(X,X)) = nand(nand(nand(nand(X4,X3),X3),X2),nand(X,nand(X2,X4))),
    inference(symmetry,[status(thm)],[c896]) ).

cnf(c898,plain,
    nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(nand(X4,X3),X3),X2),X)) = nand(nand(nand(nand(X4,X3),X3),X2),nand(X,nand(X2,X4))),
    inference(transitivity,[status(thm)],[c847,c897]) ).

cnf(c899,plain,
    nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(nand(X3,X2),X2),X),X2)) = nand(nand(nand(nand(X3,X2),X2),X),nand(X2,nand(X,X3))),
    inference(substitution,[status(thm)],[c898]) ).

cnf(c900,plain,
    nand(nand(nand(nand(X3,X2),X2),X),nand(X2,nand(X,X3))) = nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(nand(X3,X2),X2),X),X2)),
    inference(symmetry,[status(thm)],[c899]) ).

cnf(c901,plain,
    nand(nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2)),nand(nand(nand(nand(X3,X2),X2),X),nand(X2,nand(X,X3)))) = nand(nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2)),nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(nand(X3,X2),X2),X),X2))),
    inference(congruence,[status(thm)],[c900]) ).

cnf(c902,plain,
    nand(nand(X4,nand(X3,X2)),nand(X,nand(X4,X2))) = nand(nand(X,nand(X4,X2)),nand(X4,nand(X3,X2))),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c903,plain,
    nand(X4,nand(nand(X4,nand(X3,X2)),nand(X,nand(X4,X2)))) = nand(X4,nand(nand(X,nand(X4,X2)),nand(X4,nand(X3,X2)))),
    inference(congruence,[status(thm)],[c902]) ).

cnf(c904,plain,
    nand(X4,nand(nand(X,nand(X4,X2)),nand(X4,nand(X3,X2)))) = nand(nand(nand(X,nand(X4,X2)),nand(X4,nand(X3,X2))),X4),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c905,plain,
    nand(X2,X) = nand(X,X2),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c906,plain,
    nand(X,nand(X3,X2)) = nand(X,nand(X2,X3)),
    inference(congruence,[status(thm)],[c905]) ).

cnf(c907,plain,
    nand(X3,nand(X,nand(X3,X2))) = nand(X3,nand(X,nand(X2,X3))),
    inference(congruence,[status(thm)],[c906]) ).

cnf(c908,plain,
    nand(nand(X4,nand(X3,X2)),nand(X4,nand(X,nand(X4,X2)))) = nand(nand(X4,nand(X3,X2)),nand(X4,nand(X,nand(X2,X4)))),
    inference(congruence,[status(thm)],[c907]) ).

cnf(c909,plain,
    nand(X,nand(X2,X3)) = nand(nand(X2,X3),X),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c910,plain,
    nand(X3,nand(X,nand(X2,X3))) = nand(X3,nand(nand(X2,X3),X)),
    inference(congruence,[status(thm)],[c909]) ).

cnf(c911,plain,
    nand(nand(X4,nand(X3,X2)),nand(X4,nand(X,nand(X2,X4)))) = nand(nand(X4,nand(X3,X2)),nand(X4,nand(nand(X2,X4),X))),
    inference(congruence,[status(thm)],[c910]) ).

cnf(c912,plain,
    nand(nand(X,X3),nand(X3,nand(X2,X))) = X3,
    inference(substitution,[status(thm)],[c281]) ).

cnf(c913,plain,
    X3 = nand(nand(X,X3),nand(X3,nand(X2,X))),
    inference(symmetry,[status(thm)],[c912]) ).

cnf(c914,plain,
    nand(X4,nand(nand(X2,X4),X)) = nand(nand(nand(X2,X4),nand(X4,nand(X3,X2))),nand(nand(X2,X4),X)),
    inference(congruence,[status(thm)],[c913]) ).

cnf(c915,plain,
    nand(nand(X4,nand(X3,X2)),nand(X4,nand(nand(X2,X4),X))) = nand(nand(X4,nand(X3,X2)),nand(nand(nand(X2,X4),nand(X4,nand(X3,X2))),nand(nand(X2,X4),X))),
    inference(congruence,[status(thm)],[c914]) ).

cnf(c916,plain,
    nand(nand(X4,nand(X3,X2)),nand(nand(nand(X2,X4),nand(X4,nand(X3,X2))),nand(nand(X2,X4),X))) = nand(nand(X2,X4),nand(X4,nand(X3,X2))),
    inference(substitution,[status(thm)],[c758]) ).

cnf(c917,plain,
    nand(nand(X,X3),nand(X3,nand(X2,X))) = X3,
    inference(substitution,[status(thm)],[c281]) ).

cnf(c918,plain,
    nand(nand(X4,nand(X3,X2)),nand(nand(nand(X2,X4),nand(X4,nand(X3,X2))),nand(nand(X2,X4),X))) = X4,
    inference(transitivity,[status(thm)],[c916,c917]) ).

cnf(c919,plain,
    nand(nand(X4,nand(X3,X2)),nand(X4,nand(nand(X2,X4),X))) = X4,
    inference(transitivity,[status(thm)],[c915,c918]) ).

cnf(c920,plain,
    nand(nand(X4,nand(X3,X2)),nand(X4,nand(X,nand(X2,X4)))) = X4,
    inference(transitivity,[status(thm)],[c911,c919]) ).

cnf(c921,plain,
    nand(nand(X4,nand(X3,X2)),nand(X4,nand(X,nand(X4,X2)))) = X4,
    inference(transitivity,[status(thm)],[c908,c920]) ).

cnf(c922,plain,
    X4 = nand(nand(X4,nand(X3,X2)),nand(X4,nand(X,nand(X4,X2)))),
    inference(symmetry,[status(thm)],[c921]) ).

cnf(c923,plain,
    nand(nand(nand(X,nand(X4,X2)),nand(X4,nand(X3,X2))),X4) = nand(nand(nand(X,nand(X4,X2)),nand(X4,nand(X3,X2))),nand(nand(X4,nand(X3,X2)),nand(X4,nand(X,nand(X4,X2))))),
    inference(congruence,[status(thm)],[c922]) ).

cnf(c924,plain,
    nand(nand(nand(X,nand(X4,X2)),nand(X4,nand(X3,X2))),nand(nand(X4,nand(X3,X2)),nand(X4,nand(X,nand(X4,X2))))) = nand(X4,nand(X3,X2)),
    inference(substitution,[status(thm)],[c281]) ).

cnf(c925,plain,
    nand(nand(nand(X,nand(X4,X2)),nand(X4,nand(X3,X2))),X4) = nand(X4,nand(X3,X2)),
    inference(transitivity,[status(thm)],[c923,c924]) ).

cnf(c926,plain,
    nand(X4,nand(nand(X,nand(X4,X2)),nand(X4,nand(X3,X2)))) = nand(X4,nand(X3,X2)),
    inference(transitivity,[status(thm)],[c904,c925]) ).

cnf(c927,plain,
    nand(X4,nand(nand(X4,nand(X3,X2)),nand(X,nand(X4,X2)))) = nand(X4,nand(X3,X2)),
    inference(transitivity,[status(thm)],[c903,c926]) ).

cnf(c928,plain,
    nand(X3,nand(nand(X3,nand(X2,X)),nand(X3,nand(X3,X)))) = nand(X3,nand(X2,X)),
    inference(substitution,[status(thm)],[c927]) ).

cnf(c929,plain,
    nand(X3,nand(X2,X)) = nand(X3,nand(nand(X3,nand(X2,X)),nand(X3,nand(X3,X)))),
    inference(symmetry,[status(thm)],[c928]) ).

cnf(c930,plain,
    nand(nand(X3,nand(X2,X)),nand(X3,nand(X2,X))) = nand(nand(X3,nand(X2,X)),nand(X3,nand(nand(X3,nand(X2,X)),nand(X3,nand(X3,X))))),
    inference(congruence,[status(thm)],[c929]) ).

cnf(c931,plain,
    nand(nand(X3,nand(X2,X)),nand(X3,nand(nand(X3,nand(X2,X)),nand(X3,nand(X3,X))))) = nand(nand(X3,nand(X2,X)),nand(X3,nand(X3,X))),
    inference(substitution,[status(thm)],[c325]) ).

cnf(c932,plain,
    nand(nand(X3,nand(X2,X)),nand(X3,nand(X2,X))) = nand(nand(X3,nand(X2,X)),nand(X3,nand(X3,X))),
    inference(transitivity,[status(thm)],[c930,c931]) ).

cnf(c933,plain,
    nand(nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2)),nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2))) = nand(nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2)),nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(nand(X3,X2),X2),X),X2))),
    inference(substitution,[status(thm)],[c932]) ).

cnf(c934,plain,
    nand(nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2)),nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(nand(X3,X2),X2),X),X2))) = nand(nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2)),nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2))),
    inference(symmetry,[status(thm)],[c933]) ).

cnf(c935,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X3,X2),X),X3)),nand(nand(X3,X2),nand(nand(nand(X3,X2),X),X3))) = nand(nand(nand(X3,X2),X),X3),
    inference(substitution,[status(thm)],[c840]) ).

cnf(c936,plain,
    nand(nand(nand(X3,X2),X),X3) = nand(nand(nand(X3,X2),nand(nand(nand(X3,X2),X),X3)),nand(nand(X3,X2),nand(nand(nand(X3,X2),X),X3))),
    inference(symmetry,[status(thm)],[c935]) ).

cnf(c937,plain,
    nand(nand(nand(nand(X3,X2),X),X3),nand(nand(nand(X3,X2),X),X3)) = nand(nand(nand(nand(X3,X2),X),X3),nand(nand(nand(X3,X2),nand(nand(nand(X3,X2),X),X3)),nand(nand(X3,X2),nand(nand(nand(X3,X2),X),X3)))),
    inference(congruence,[status(thm)],[c936]) ).

cnf(c938,plain,
    nand(nand(nand(nand(X3,X2),X),X3),nand(nand(nand(X3,X2),nand(nand(nand(X3,X2),X),X3)),nand(nand(X3,X2),nand(nand(nand(X3,X2),X),X3)))) = nand(nand(X3,X2),nand(nand(nand(X3,X2),X),X3)),
    inference(substitution,[status(thm)],[c758]) ).

cnf(c939,plain,
    nand(nand(nand(nand(X3,X2),X),X3),nand(nand(nand(X3,X2),X),X3)) = nand(nand(X3,X2),nand(nand(nand(X3,X2),X),X3)),
    inference(transitivity,[status(thm)],[c937,c938]) ).

cnf(c940,plain,
    nand(nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2)),nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2))) = nand(nand(nand(X3,X2),X2),nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2))),
    inference(substitution,[status(thm)],[c939]) ).

cnf(c941,plain,
    nand(nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2)),nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(nand(X3,X2),X2),X),X2))) = nand(nand(nand(X3,X2),X2),nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2))),
    inference(transitivity,[status(thm)],[c934,c940]) ).

cnf(c942,plain,
    nand(nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2)),nand(nand(nand(nand(X3,X2),X2),X),nand(X2,nand(X,X3)))) = nand(nand(nand(X3,X2),X2),nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2))),
    inference(transitivity,[status(thm)],[c901,c941]) ).

cnf(c943,plain,
    nand(nand(nand(nand(nand(X3,X2),X2),X),nand(X2,nand(X,X3))),nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2))) = nand(nand(nand(X3,X2),X2),nand(nand(nand(nand(X3,X2),X2),X),nand(X3,X2))),
    inference(transitivity,[status(thm)],[c845,c942]) ).

cnf(c944,plain,
    nand(nand(nand(nand(nand(X,X3),X3),X2),nand(X3,nand(X2,X))),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3))) = nand(nand(nand(X,X3),X3),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3))),
    inference(substitution,[status(thm)],[c943]) ).

cnf(c945,plain,
    nand(nand(nand(X,X3),X3),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3))) = nand(nand(nand(nand(nand(X,X3),X3),X2),nand(X3,nand(X2,X))),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3))),
    inference(symmetry,[status(thm)],[c944]) ).

cnf(c946,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(nand(X,X3),X3),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3)))) = nand(nand(X3,nand(X2,X)),nand(nand(nand(nand(nand(X,X3),X3),X2),nand(X3,nand(X2,X))),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3)))),
    inference(congruence,[status(thm)],[c945]) ).

cnf(c947,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(nand(nand(nand(X,X3),X3),X2),nand(X3,nand(X2,X))),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3)))) = nand(nand(nand(nand(X,X3),X3),X2),nand(X3,nand(X2,X))),
    inference(substitution,[status(thm)],[c758]) ).

cnf(c948,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(nand(X,X3),X3),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3)))) = nand(nand(nand(nand(X,X3),X3),X2),nand(X3,nand(X2,X))),
    inference(transitivity,[status(thm)],[c946,c947]) ).

cnf(c949,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(X3,nand(X2,X)),nand(nand(nand(X,X3),X3),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3))))) = nand(nand(X3,nand(X2,X)),nand(nand(nand(nand(X,X3),X3),X2),nand(X3,nand(X2,X)))),
    inference(congruence,[status(thm)],[c948]) ).

cnf(c950,plain,
    nand(nand(X4,nand(X3,X2)),nand(nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))),nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))))) = nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))),
    inference(substitution,[status(thm)],[c864]) ).

cnf(c951,plain,
    nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))) = nand(nand(X4,nand(X3,X2)),nand(nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))),nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))))),
    inference(symmetry,[status(thm)],[c950]) ).

cnf(c952,plain,
    nand(nand(X4,nand(X3,X2)),nand(nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))),nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))))) = nand(nand(X4,nand(X3,X2)),nand(nand(X4,nand(X3,X2)),nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))))),
    inference(substitution,[status(thm)],[c341]) ).

cnf(c953,plain,
    nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))))) = nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))),
    inference(substitution,[status(thm)],[c325]) ).

cnf(c954,plain,
    nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))) = nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))))),
    inference(symmetry,[status(thm)],[c953]) ).

cnf(c955,plain,
    nand(nand(X3,nand(X2,X)),nand(X4,nand(nand(X,X3),X3))) = nand(nand(X4,nand(nand(X,X3),X3)),nand(X3,nand(X2,X))),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c956,plain,
    nand(X4,nand(nand(X3,nand(X2,X)),nand(X4,nand(nand(X,X3),X3)))) = nand(X4,nand(nand(X4,nand(nand(X,X3),X3)),nand(X3,nand(X2,X)))),
    inference(congruence,[status(thm)],[c955]) ).

cnf(c957,plain,
    nand(X2,nand(X2,nand(X2,X))) = nand(nand(X2,nand(X2,X)),X2),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c958,plain,
    X2 = nand(nand(X2,X),nand(X2,nand(X2,X))),
    inference(symmetry,[status(thm)],[c198]) ).

cnf(c959,plain,
    nand(nand(X2,nand(X2,X)),X2) = nand(nand(X2,nand(X2,X)),nand(nand(X2,X),nand(X2,nand(X2,X)))),
    inference(congruence,[status(thm)],[c958]) ).

cnf(c960,plain,
    nand(nand(X2,nand(X2,X)),nand(nand(X2,X),nand(X2,nand(X2,X)))) = nand(X2,X),
    inference(substitution,[status(thm)],[c422]) ).

cnf(c961,plain,
    nand(nand(X2,nand(X2,X)),X2) = nand(X2,X),
    inference(transitivity,[status(thm)],[c959,c960]) ).

cnf(c962,plain,
    nand(X2,nand(X2,nand(X2,X))) = nand(X2,X),
    inference(transitivity,[status(thm)],[c957,c961]) ).

cnf(c963,plain,
    nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(X4,nand(nand(X,X3),X3)),nand(X3,nand(X2,X))))) = nand(nand(X4,nand(nand(X,X3),X3)),nand(X3,nand(X2,X))),
    inference(substitution,[status(thm)],[c962]) ).

cnf(c964,plain,
    nand(nand(X4,nand(nand(X,X3),X3)),nand(X3,nand(X2,X))) = nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(X4,nand(nand(X,X3),X3)),nand(X3,nand(X2,X))))),
    inference(symmetry,[status(thm)],[c963]) ).

cnf(c965,plain,
    nand(X4,nand(nand(X4,nand(nand(X,X3),X3)),nand(X3,nand(X2,X)))) = nand(X4,nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(X4,nand(nand(X,X3),X3)),nand(X3,nand(X2,X)))))),
    inference(congruence,[status(thm)],[c964]) ).

cnf(c966,plain,
    nand(X4,nand(X4,nand(nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3))),nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3)))))) = nand(X4,nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3)))),
    inference(substitution,[status(thm)],[c866]) ).

cnf(c967,plain,
    nand(X4,nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3)))) = nand(X4,nand(X4,nand(nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3))),nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3)))))),
    inference(symmetry,[status(thm)],[c966]) ).

cnf(c968,plain,
    nand(nand(X2,X),nand(X,nand(nand(X2,X),X))) = nand(nand(X2,X),nand(X2,X)),
    inference(substitution,[status(thm)],[c332]) ).

cnf(c969,plain,
    nand(nand(X2,X),nand(X2,X)) = nand(nand(X2,X),nand(X,nand(nand(X2,X),X))),
    inference(symmetry,[status(thm)],[c968]) ).

cnf(c970,plain,
    nand(nand(X2,X),nand(nand(X2,X),nand(X2,X))) = nand(nand(X2,X),nand(nand(X2,X),nand(X,nand(nand(X2,X),X)))),
    inference(congruence,[status(thm)],[c969]) ).

cnf(c971,plain,
    nand(X2,nand(nand(X2,X),nand(nand(X2,X),nand(X2,X)))) = nand(X2,nand(nand(X2,X),nand(nand(X2,X),nand(X,nand(nand(X2,X),X))))),
    inference(congruence,[status(thm)],[c970]) ).

cnf(c972,plain,
    nand(X2,nand(nand(X2,X),nand(nand(X2,X),nand(X,nand(nand(X2,X),X))))) = nand(X2,X2),
    inference(substitution,[status(thm)],[c889]) ).

cnf(c973,plain,
    nand(X2,nand(nand(X2,X),nand(nand(X2,X),nand(X2,X)))) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c971,c972]) ).

cnf(c974,plain,
    nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))),nand(nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))),nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4))))))) = nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4)))),
    inference(substitution,[status(thm)],[c973]) ).

cnf(c975,plain,
    nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4)))) = nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))),nand(nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))),nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4))))))),
    inference(symmetry,[status(thm)],[c974]) ).

cnf(c976,plain,
    nand(nand(X3,X2),nand(X2,X)) = nand(nand(X2,X),nand(X3,X2)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c977,plain,
    nand(nand(nand(X4,X3),nand(X3,X2)),nand(nand(X3,X2),nand(X,X2))) = nand(nand(nand(X3,X2),nand(X4,X3)),nand(nand(X3,X2),nand(X,X2))),
    inference(congruence,[status(thm)],[c976]) ).

cnf(c978,plain,
    nand(nand(X3,X2),nand(nand(X4,X3),nand(nand(X3,X2),nand(X,X2)))) = nand(nand(X3,X2),nand(X,X2)),
    inference(substitution,[status(thm)],[c460]) ).

cnf(c979,plain,
    nand(nand(X3,X2),nand(X,X2)) = nand(nand(X3,X2),nand(nand(X4,X3),nand(nand(X3,X2),nand(X,X2)))),
    inference(symmetry,[status(thm)],[c978]) ).

cnf(c980,plain,
    nand(nand(nand(X3,X2),nand(X4,X3)),nand(nand(X3,X2),nand(X,X2))) = nand(nand(nand(X3,X2),nand(X4,X3)),nand(nand(X3,X2),nand(nand(X4,X3),nand(nand(X3,X2),nand(X,X2))))),
    inference(congruence,[status(thm)],[c979]) ).

cnf(c981,plain,
    nand(nand(nand(X3,X2),nand(X4,X3)),nand(nand(X3,X2),nand(nand(X4,X3),nand(nand(X3,X2),nand(X,X2))))) = nand(X3,X2),
    inference(substitution,[status(thm)],[c514]) ).

cnf(c982,plain,
    nand(nand(nand(X3,X2),nand(X4,X3)),nand(nand(X3,X2),nand(X,X2))) = nand(X3,X2),
    inference(transitivity,[status(thm)],[c980,c981]) ).

cnf(c983,plain,
    nand(nand(nand(X4,X3),nand(X3,X2)),nand(nand(X3,X2),nand(X,X2))) = nand(X3,X2),
    inference(transitivity,[status(thm)],[c977,c982]) ).

cnf(c984,plain,
    nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))) = nand(X3,nand(X2,X4)),
    inference(substitution,[status(thm)],[c983]) ).

cnf(c985,plain,
    nand(nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))),nand(nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))),nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))))) = nand(nand(X3,nand(X2,X4)),nand(nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))),nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))))),
    inference(congruence,[status(thm)],[c984]) ).

cnf(c986,plain,
    nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))),nand(nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))),nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4))))))) = nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))),nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4))))))),
    inference(congruence,[status(thm)],[c985]) ).

cnf(c987,plain,
    nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))) = nand(X3,nand(X2,X4)),
    inference(substitution,[status(thm)],[c983]) ).

cnf(c988,plain,
    nand(nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))),nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4))))) = nand(nand(X3,nand(X2,X4)),nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4))))),
    inference(congruence,[status(thm)],[c987]) ).

cnf(c989,plain,
    nand(nand(X3,nand(X2,X4)),nand(nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))),nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))))) = nand(nand(X3,nand(X2,X4)),nand(nand(X3,nand(X2,X4)),nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))))),
    inference(congruence,[status(thm)],[c988]) ).

cnf(c990,plain,
    nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))),nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4))))))) = nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(nand(X3,nand(X2,X4)),nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4))))))),
    inference(congruence,[status(thm)],[c989]) ).

cnf(c991,plain,
    nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))) = nand(X3,nand(X2,X4)),
    inference(substitution,[status(thm)],[c983]) ).

cnf(c992,plain,
    nand(nand(X3,nand(X2,X4)),nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4))))) = nand(nand(X3,nand(X2,X4)),nand(X3,nand(X2,X4))),
    inference(congruence,[status(thm)],[c991]) ).

cnf(c993,plain,
    nand(nand(X3,nand(X2,X4)),nand(nand(X3,nand(X2,X4)),nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))))) = nand(nand(X3,nand(X2,X4)),nand(nand(X3,nand(X2,X4)),nand(X3,nand(X2,X4)))),
    inference(congruence,[status(thm)],[c992]) ).

cnf(c994,plain,
    nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(nand(X3,nand(X2,X4)),nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4))))))) = nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(nand(X3,nand(X2,X4)),nand(X3,nand(X2,X4))))),
    inference(congruence,[status(thm)],[c993]) ).

cnf(c995,plain,
    nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3))) = nand(nand(X2,nand(X,X3)),nand(X2,nand(X,X3))),
    inference(substitution,[status(thm)],[c806]) ).

cnf(c996,plain,
    nand(nand(X2,nand(X,X3)),nand(X2,nand(X,X3))) = nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3))),
    inference(symmetry,[status(thm)],[c995]) ).

cnf(c997,plain,
    nand(nand(X2,nand(X,X3)),nand(nand(X2,nand(X,X3)),nand(X2,nand(X,X3)))) = nand(nand(X2,nand(X,X3)),nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3)))),
    inference(congruence,[status(thm)],[c996]) ).

cnf(c998,plain,
    nand(nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3))),nand(nand(X2,nand(X,X3)),nand(nand(X2,nand(X,X3)),nand(X2,nand(X,X3))))) = nand(nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3))),nand(nand(X2,nand(X,X3)),nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3))))),
    inference(congruence,[status(thm)],[c997]) ).

cnf(c999,plain,
    nand(nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3))),nand(nand(X2,nand(X,X3)),nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3))))) = nand(X2,nand(X,X3)),
    inference(substitution,[status(thm)],[c422]) ).

cnf(c1000,plain,
    nand(nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3))),nand(nand(X2,nand(X,X3)),nand(nand(X2,nand(X,X3)),nand(X2,nand(X,X3))))) = nand(X2,nand(X,X3)),
    inference(transitivity,[status(thm)],[c998,c999]) ).

cnf(c1001,plain,
    nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(nand(X3,nand(X2,X4)),nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4))))))) = nand(X3,nand(X2,X4)),
    inference(transitivity,[status(thm)],[c994,c1000]) ).

cnf(c1002,plain,
    nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))),nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4))))))) = nand(X3,nand(X2,X4)),
    inference(transitivity,[status(thm)],[c990,c1001]) ).

cnf(c1003,plain,
    nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))),nand(nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4)))),nand(nand(nand(nand(X4,X3),X3),nand(X3,nand(X2,X4))),nand(nand(X3,nand(X2,X4)),nand(X,nand(X2,X4))))))) = nand(X3,nand(X2,X4)),
    inference(transitivity,[status(thm)],[c986,c1002]) ).

cnf(c1004,plain,
    nand(nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3))),nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3)))) = nand(X2,nand(X,X3)),
    inference(transitivity,[status(thm)],[c975,c1003]) ).

cnf(c1005,plain,
    nand(X4,nand(nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3))),nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3))))) = nand(X4,nand(X2,nand(X,X3))),
    inference(congruence,[status(thm)],[c1004]) ).

cnf(c1006,plain,
    nand(X4,nand(X4,nand(nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3))),nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3)))))) = nand(X4,nand(X4,nand(X2,nand(X,X3)))),
    inference(congruence,[status(thm)],[c1005]) ).

cnf(c1007,plain,
    nand(X4,nand(nand(nand(X3,X2),X2),nand(X2,nand(X,X3)))) = nand(X4,nand(X4,nand(X2,nand(X,X3)))),
    inference(transitivity,[status(thm)],[c967,c1006]) ).

cnf(c1008,plain,
    nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(nand(X,X3),X3),nand(X3,nand(X2,X)))) = nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(X4,nand(nand(X,X3),X3)),nand(X3,nand(X2,X)))),
    inference(substitution,[status(thm)],[c1007]) ).

cnf(c1009,plain,
    nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(X4,nand(nand(X,X3),X3)),nand(X3,nand(X2,X)))) = nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(nand(X,X3),X3),nand(X3,nand(X2,X)))),
    inference(symmetry,[status(thm)],[c1008]) ).

cnf(c1010,plain,
    nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(X4,nand(nand(X,X3),X3)),nand(X3,nand(X2,X))))) = nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(nand(X,X3),X3),nand(X3,nand(X2,X))))),
    inference(congruence,[status(thm)],[c1009]) ).

cnf(c1011,plain,
    nand(X4,nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(X4,nand(nand(X,X3),X3)),nand(X3,nand(X2,X)))))) = nand(X4,nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(nand(X,X3),X3),nand(X3,nand(X2,X)))))),
    inference(congruence,[status(thm)],[c1010]) ).

cnf(c1012,plain,
    nand(X4,nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(nand(X,X3),X3),nand(X3,nand(X2,X)))))) = nand(X4,X4),
    inference(substitution,[status(thm)],[c889]) ).

cnf(c1013,plain,
    nand(X4,nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(X4,nand(nand(X,X3),X3)),nand(nand(X4,nand(nand(X,X3),X3)),nand(X3,nand(X2,X)))))) = nand(X4,X4),
    inference(transitivity,[status(thm)],[c1011,c1012]) ).

cnf(c1014,plain,
    nand(X4,nand(nand(X4,nand(nand(X,X3),X3)),nand(X3,nand(X2,X)))) = nand(X4,X4),
    inference(transitivity,[status(thm)],[c965,c1013]) ).

cnf(c1015,plain,
    nand(X4,nand(nand(X3,nand(X2,X)),nand(X4,nand(nand(X,X3),X3)))) = nand(X4,X4),
    inference(transitivity,[status(thm)],[c956,c1014]) ).

cnf(c1016,plain,
    nand(X,nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4)))) = nand(X,X),
    inference(substitution,[status(thm)],[c1015]) ).

cnf(c1017,plain,
    nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))))) = nand(nand(X4,nand(X3,X2)),nand(X,X)),
    inference(congruence,[status(thm)],[c1016]) ).

cnf(c1018,plain,
    nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))) = nand(nand(X4,nand(X3,X2)),nand(X,X)),
    inference(transitivity,[status(thm)],[c954,c1017]) ).

cnf(c1019,plain,
    nand(nand(X4,nand(X3,X2)),nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4)))) = nand(nand(X4,nand(X3,X2)),nand(nand(X4,nand(X3,X2)),nand(X,X))),
    inference(congruence,[status(thm)],[c1018]) ).

cnf(c1020,plain,
    nand(nand(X4,nand(X3,X2)),nand(nand(X,X),nand(X,X))) = nand(nand(X4,nand(X3,X2)),nand(nand(X4,nand(X3,X2)),nand(X,X))),
    inference(substitution,[status(thm)],[c341]) ).

cnf(c1021,plain,
    nand(nand(X4,nand(X3,X2)),nand(nand(X4,nand(X3,X2)),nand(X,X))) = nand(nand(X4,nand(X3,X2)),nand(nand(X,X),nand(X,X))),
    inference(symmetry,[status(thm)],[c1020]) ).

cnf(c1022,plain,
    nand(nand(X4,nand(X3,X2)),nand(nand(X,X),nand(X,X))) = nand(nand(X4,nand(X3,X2)),X),
    inference(congruence,[status(thm)],[c64]) ).

cnf(c1023,plain,
    nand(X,nand(X4,nand(X3,X2))) = nand(nand(X4,nand(X3,X2)),X),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c1024,plain,
    nand(nand(X4,nand(X3,X2)),X) = nand(X,nand(X4,nand(X3,X2))),
    inference(symmetry,[status(thm)],[c1023]) ).

cnf(c1025,plain,
    nand(nand(X4,nand(X3,X2)),nand(nand(X,X),nand(X,X))) = nand(X,nand(X4,nand(X3,X2))),
    inference(transitivity,[status(thm)],[c1022,c1024]) ).

cnf(c1026,plain,
    nand(nand(X4,nand(X3,X2)),nand(nand(X4,nand(X3,X2)),nand(X,X))) = nand(X,nand(X4,nand(X3,X2))),
    inference(transitivity,[status(thm)],[c1021,c1025]) ).

cnf(c1027,plain,
    nand(nand(X4,nand(X3,X2)),nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4)))) = nand(X,nand(X4,nand(X3,X2))),
    inference(transitivity,[status(thm)],[c1019,c1026]) ).

cnf(c1028,plain,
    nand(nand(X4,nand(X3,X2)),nand(nand(X4,nand(X3,X2)),nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))))) = nand(nand(X4,nand(X3,X2)),nand(X,nand(X4,nand(X3,X2)))),
    inference(congruence,[status(thm)],[c1027]) ).

cnf(c1029,plain,
    nand(nand(X4,nand(X3,X2)),nand(nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))),nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))))) = nand(nand(X4,nand(X3,X2)),nand(X,nand(X4,nand(X3,X2)))),
    inference(transitivity,[status(thm)],[c952,c1028]) ).

cnf(c1030,plain,
    nand(nand(X4,nand(X3,X2)),nand(X,nand(nand(X2,X4),X4))) = nand(nand(X4,nand(X3,X2)),nand(X,nand(X4,nand(X3,X2)))),
    inference(transitivity,[status(thm)],[c951,c1029]) ).

cnf(c1031,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(nand(nand(X,X3),X3),X2),nand(nand(X,X3),X3))) = nand(nand(X3,nand(X2,X)),nand(nand(nand(nand(X,X3),X3),X2),nand(X3,nand(X2,X)))),
    inference(substitution,[status(thm)],[c1030]) ).

cnf(c1032,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(nand(nand(X,X3),X3),X2),nand(X3,nand(X2,X)))) = nand(nand(X3,nand(X2,X)),nand(nand(nand(nand(X,X3),X3),X2),nand(nand(X,X3),X3))),
    inference(symmetry,[status(thm)],[c1031]) ).

cnf(c1033,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(nand(nand(X,X3),X3),X2),nand(nand(X,X3),X3))) = nand(nand(X3,nand(X2,X)),nand(nand(nand(nand(X,X3),X3),X2),nand(nand(nand(X,X3),X3),X2))),
    inference(substitution,[status(thm)],[c1018]) ).

cnf(c1034,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(nand(nand(X,X3),X3),X2),nand(nand(nand(X,X3),X3),X2))) = nand(nand(nand(nand(nand(X,X3),X3),X2),nand(nand(nand(X,X3),X3),X2)),nand(X3,nand(X2,X))),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c1035,plain,
    nand(nand(X2,nand(X3,nand(X2,X))),nand(nand(X3,nand(X2,X)),nand(X2,X))) = nand(X3,nand(X2,X)),
    inference(substitution,[status(thm)],[c653]) ).

cnf(c1036,plain,
    nand(X3,nand(X2,X)) = nand(nand(X2,nand(X3,nand(X2,X))),nand(nand(X3,nand(X2,X)),nand(X2,X))),
    inference(symmetry,[status(thm)],[c1035]) ).

cnf(c1037,plain,
    nand(nand(nand(nand(nand(X,X3),X3),X2),nand(nand(nand(X,X3),X3),X2)),nand(X3,nand(X2,X))) = nand(nand(nand(nand(nand(X,X3),X3),X2),nand(nand(nand(X,X3),X3),X2)),nand(nand(X2,nand(X3,nand(X2,X))),nand(nand(X3,nand(X2,X)),nand(X2,X)))),
    inference(congruence,[status(thm)],[c1036]) ).

cnf(c1038,plain,
    nand(nand(X4,nand(X3,nand(X4,X2))),nand(X,nand(nand(X4,nand(X3,nand(X4,X2))),nand(X,nand(X4,X2))))) = nand(nand(X4,nand(X3,nand(X4,X2))),nand(X,nand(X4,X2))),
    inference(substitution,[status(thm)],[c325]) ).

cnf(c1039,plain,
    nand(nand(X4,nand(X3,nand(X4,X2))),nand(X,nand(X4,X2))) = nand(nand(X4,nand(X3,nand(X4,X2))),nand(X,nand(nand(X4,nand(X3,nand(X4,X2))),nand(X,nand(X4,X2))))),
    inference(symmetry,[status(thm)],[c1038]) ).

cnf(c1040,plain,
    nand(nand(X3,nand(X2,nand(X3,X))),nand(X4,nand(X3,X))) = nand(nand(X4,nand(X3,X)),nand(X3,nand(X2,nand(X3,X)))),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c1041,plain,
    nand(X4,nand(nand(X3,nand(X2,nand(X3,X))),nand(X4,nand(X3,X)))) = nand(X4,nand(nand(X4,nand(X3,X)),nand(X3,nand(X2,nand(X3,X))))),
    inference(congruence,[status(thm)],[c1040]) ).

cnf(c1042,plain,
    nand(nand(X4,nand(X3,X)),nand(nand(X4,nand(X3,X)),nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))))) = nand(nand(X4,nand(X3,X)),nand(X3,nand(X2,nand(X3,X)))),
    inference(substitution,[status(thm)],[c866]) ).

cnf(c1043,plain,
    nand(nand(X4,nand(X3,X)),nand(X3,nand(X2,nand(X3,X)))) = nand(nand(X4,nand(X3,X)),nand(nand(X4,nand(X3,X)),nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))))),
    inference(symmetry,[status(thm)],[c1042]) ).

cnf(c1044,plain,
    nand(X4,nand(nand(X4,nand(X3,X)),nand(X3,nand(X2,nand(X3,X))))) = nand(X4,nand(nand(X4,nand(X3,X)),nand(nand(X4,nand(X3,X)),nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X))))))),
    inference(congruence,[status(thm)],[c1043]) ).

cnf(c1045,plain,
    nand(nand(X4,X3),nand(nand(X3,X2),nand(nand(X4,nand(X,nand(X4,X3))),nand(X4,nand(X,nand(X4,X3)))))) = nand(nand(nand(X3,X2),nand(nand(X4,nand(X,nand(X4,X3))),nand(X4,nand(X,nand(X4,X3))))),nand(X4,X3)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c1046,plain,
    nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,nand(X,nand(X3,X2)))) = nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),
    inference(symmetry,[status(thm)],[c666]) ).

cnf(c1047,plain,
    nand(nand(X3,X2),nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))))) = nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),
    inference(substitution,[status(thm)],[c864]) ).

cnf(c1048,plain,
    nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))) = nand(nand(X3,X2),nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))))),
    inference(symmetry,[status(thm)],[c1047]) ).

cnf(c1049,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2)))) = nand(nand(X,nand(X3,X2)),nand(nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(X,nand(X3,X2))),nand(X,nand(X3,X2)))),
    inference(substitution,[status(thm)],[c681]) ).

cnf(c1050,plain,
    nand(nand(X3,X2),nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))))) = nand(nand(X3,X2),nand(nand(X,nand(X3,X2)),nand(nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(X,nand(X3,X2))),nand(X,nand(X3,X2))))),
    inference(congruence,[status(thm)],[c1049]) ).

cnf(c1051,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(X,nand(X3,X2))) = nand(X3,nand(X,nand(X3,X2))),
    inference(substitution,[status(thm)],[c658]) ).

cnf(c1052,plain,
    nand(nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(X,nand(X3,X2))),nand(X,nand(X3,X2))) = nand(nand(X3,nand(X,nand(X3,X2))),nand(X,nand(X3,X2))),
    inference(congruence,[status(thm)],[c1051]) ).

cnf(c1053,plain,
    nand(nand(X,nand(X3,X2)),nand(nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(X,nand(X3,X2))),nand(X,nand(X3,X2)))) = nand(nand(X,nand(X3,X2)),nand(nand(X3,nand(X,nand(X3,X2))),nand(X,nand(X3,X2)))),
    inference(congruence,[status(thm)],[c1052]) ).

cnf(c1054,plain,
    nand(nand(X3,X2),nand(nand(X,nand(X3,X2)),nand(nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(X,nand(X3,X2))),nand(X,nand(X3,X2))))) = nand(nand(X3,X2),nand(nand(X,nand(X3,X2)),nand(nand(X3,nand(X,nand(X3,X2))),nand(X,nand(X3,X2))))),
    inference(congruence,[status(thm)],[c1053]) ).

cnf(c1055,plain,
    nand(nand(X,nand(X3,X2)),nand(nand(X3,nand(X,nand(X3,X2))),nand(X,nand(X3,X2)))) = nand(X3,nand(X,nand(X3,X2))),
    inference(substitution,[status(thm)],[c432]) ).

cnf(c1056,plain,
    nand(nand(X3,X2),nand(nand(X,nand(X3,X2)),nand(nand(X3,nand(X,nand(X3,X2))),nand(X,nand(X3,X2))))) = nand(nand(X3,X2),nand(X3,nand(X,nand(X3,X2)))),
    inference(congruence,[status(thm)],[c1055]) ).

cnf(c1057,plain,
    nand(nand(X3,X2),nand(nand(X,nand(X3,X2)),nand(nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(X,nand(X3,X2))),nand(X,nand(X3,X2))))) = nand(nand(X3,X2),nand(X3,nand(X,nand(X3,X2)))),
    inference(transitivity,[status(thm)],[c1054,c1056]) ).

cnf(c1058,plain,
    nand(nand(X3,X2),nand(nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))),nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))))) = nand(nand(X3,X2),nand(X3,nand(X,nand(X3,X2)))),
    inference(transitivity,[status(thm)],[c1050,c1057]) ).

cnf(c1059,plain,
    nand(nand(X3,X2),nand(nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,X2)),nand(X3,X2))) = nand(nand(X3,X2),nand(X3,nand(X,nand(X3,X2)))),
    inference(transitivity,[status(thm)],[c1048,c1058]) ).

cnf(c1060,plain,
    nand(nand(X3,nand(X,nand(X3,X2))),nand(X3,nand(X,nand(X3,X2)))) = nand(nand(X3,X2),nand(X3,nand(X,nand(X3,X2)))),
    inference(transitivity,[status(thm)],[c1046,c1059]) ).

cnf(c1061,plain,
    nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X)))) = nand(nand(X3,X),nand(X3,nand(X2,nand(X3,X)))),
    inference(substitution,[status(thm)],[c1060]) ).

cnf(c1062,plain,
    nand(nand(nand(X4,nand(X3,nand(X4,X2))),nand(X4,nand(X3,nand(X4,X2)))),nand(nand(X4,X2),nand(X2,X))) = nand(nand(nand(X4,X2),nand(X4,nand(X3,nand(X4,X2)))),nand(nand(X4,X2),nand(X2,X))),
    inference(congruence,[status(thm)],[c1061]) ).

cnf(c1063,plain,
    nand(nand(X3,X2),nand(X2,X)) = nand(nand(X2,X),nand(X3,X2)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c1064,plain,
    nand(nand(X4,X2),nand(nand(X4,X3),nand(X3,X))) = nand(nand(X4,X2),nand(nand(X3,X),nand(X4,X3))),
    inference(congruence,[status(thm)],[c1063]) ).

cnf(c1065,plain,
    nand(nand(X4,X3),nand(nand(X4,X2),nand(nand(X4,X3),nand(X3,X)))) = nand(nand(X4,X3),nand(nand(X4,X2),nand(nand(X3,X),nand(X4,X3)))),
    inference(congruence,[status(thm)],[c1064]) ).

cnf(c1066,plain,
    nand(nand(X4,X2),nand(nand(X3,X),nand(X4,X3))) = nand(nand(nand(X3,X),nand(X4,X3)),nand(X4,X2)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c1067,plain,
    nand(nand(X4,X3),nand(nand(X4,X2),nand(nand(X3,X),nand(X4,X3)))) = nand(nand(X4,X3),nand(nand(nand(X3,X),nand(X4,X3)),nand(X4,X2))),
    inference(congruence,[status(thm)],[c1066]) ).

cnf(c1068,plain,
    nand(nand(X2,X),nand(nand(nand(X3,X2),nand(X2,X)),nand(X2,X))) = nand(nand(X2,X),nand(X3,X2)),
    inference(substitution,[status(thm)],[c239]) ).

cnf(c1069,plain,
    nand(nand(X2,X),nand(X3,X2)) = nand(nand(X2,X),nand(nand(nand(X3,X2),nand(X2,X)),nand(X2,X))),
    inference(symmetry,[status(thm)],[c1068]) ).

cnf(c1070,plain,
    nand(nand(nand(X3,X),nand(X4,X3)),nand(X4,X2)) = nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(X3,X)),nand(X3,X))),nand(X4,X2)),
    inference(congruence,[status(thm)],[c1069]) ).

cnf(c1071,plain,
    nand(nand(X4,X3),nand(nand(nand(X3,X),nand(X4,X3)),nand(X4,X2))) = nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(X3,X)),nand(X3,X))),nand(X4,X2))),
    inference(congruence,[status(thm)],[c1070]) ).

cnf(c1072,plain,
    nand(X2,X) = nand(nand(nand(X2,X),nand(X2,X)),X2),
    inference(symmetry,[status(thm)],[c578]) ).

cnf(c1073,plain,
    nand(nand(X3,X2),nand(X2,X)) = nand(nand(X3,X2),nand(nand(nand(X2,X),nand(X2,X)),X2)),
    inference(congruence,[status(thm)],[c1072]) ).

cnf(c1074,plain,
    nand(nand(nand(X3,X2),nand(X2,X)),nand(X2,X)) = nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(X2,X)),X2)),nand(X2,X)),
    inference(congruence,[status(thm)],[c1073]) ).

cnf(c1075,plain,
    nand(nand(X2,X),nand(nand(nand(X3,X2),nand(X2,X)),nand(X2,X))) = nand(nand(X2,X),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(X2,X)),X2)),nand(X2,X))),
    inference(congruence,[status(thm)],[c1074]) ).

cnf(c1076,plain,
    nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(X3,X)),nand(X3,X))),nand(X4,X2)) = nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(X3,X)),X3)),nand(X3,X))),nand(X4,X2)),
    inference(congruence,[status(thm)],[c1075]) ).

cnf(c1077,plain,
    nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(X3,X)),nand(X3,X))),nand(X4,X2))) = nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(X3,X)),X3)),nand(X3,X))),nand(X4,X2))),
    inference(congruence,[status(thm)],[c1076]) ).

cnf(c1078,plain,
    nand(X2,X) = nand(nand(nand(X2,X),nand(X2,X)),X2),
    inference(symmetry,[status(thm)],[c578]) ).

cnf(c1079,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(X2,X)),X2)),nand(X2,X)) = nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(X2,X)),X2)),nand(nand(nand(X2,X),nand(X2,X)),X2)),
    inference(congruence,[status(thm)],[c1078]) ).

cnf(c1080,plain,
    nand(nand(X2,X),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(X2,X)),X2)),nand(X2,X))) = nand(nand(X2,X),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(X2,X)),X2)),nand(nand(nand(X2,X),nand(X2,X)),X2))),
    inference(congruence,[status(thm)],[c1079]) ).

cnf(c1081,plain,
    nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(X3,X)),X3)),nand(X3,X))),nand(X4,X2)) = nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(X3,X)),X3)),nand(nand(nand(X3,X),nand(X3,X)),X3))),nand(X4,X2)),
    inference(congruence,[status(thm)],[c1080]) ).

cnf(c1082,plain,
    nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(X3,X)),X3)),nand(X3,X))),nand(X4,X2))) = nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(X3,X)),X3)),nand(nand(nand(X3,X),nand(X3,X)),X3))),nand(X4,X2))),
    inference(congruence,[status(thm)],[c1081]) ).

cnf(c1083,plain,
    nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))) = nand(nand(X2,X),nand(X2,X)),
    inference(substitution,[status(thm)],[c57]) ).

cnf(c1084,plain,
    nand(nand(X2,X),nand(X2,X)) = nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),
    inference(symmetry,[status(thm)],[c1083]) ).

cnf(c1085,plain,
    nand(nand(nand(X2,X),nand(X2,X)),X2) = nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2),
    inference(congruence,[status(thm)],[c1084]) ).

cnf(c1086,plain,
    nand(nand(X3,X2),nand(nand(nand(X2,X),nand(X2,X)),X2)) = nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2)),
    inference(congruence,[status(thm)],[c1085]) ).

cnf(c1087,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(X2,X)),X2)),nand(nand(nand(X2,X),nand(X2,X)),X2)) = nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(X2,X)),X2)),
    inference(congruence,[status(thm)],[c1086]) ).

cnf(c1088,plain,
    nand(nand(X2,X),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(X2,X)),X2)),nand(nand(nand(X2,X),nand(X2,X)),X2))) = nand(nand(X2,X),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(X2,X)),X2))),
    inference(congruence,[status(thm)],[c1087]) ).

cnf(c1089,plain,
    nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(X3,X)),X3)),nand(nand(nand(X3,X),nand(X3,X)),X3))),nand(X4,X2)) = nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(X3,X)),X3))),nand(X4,X2)),
    inference(congruence,[status(thm)],[c1088]) ).

cnf(c1090,plain,
    nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(X3,X)),X3)),nand(nand(nand(X3,X),nand(X3,X)),X3))),nand(X4,X2))) = nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(X3,X)),X3))),nand(X4,X2))),
    inference(congruence,[status(thm)],[c1089]) ).

cnf(c1091,plain,
    nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))) = nand(nand(X2,X),nand(X2,X)),
    inference(substitution,[status(thm)],[c57]) ).

cnf(c1092,plain,
    nand(nand(X2,X),nand(X2,X)) = nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),
    inference(symmetry,[status(thm)],[c1091]) ).

cnf(c1093,plain,
    nand(nand(nand(X2,X),nand(X2,X)),X2) = nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2),
    inference(congruence,[status(thm)],[c1092]) ).

cnf(c1094,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(X2,X)),X2)) = nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2)),
    inference(congruence,[status(thm)],[c1093]) ).

cnf(c1095,plain,
    nand(nand(X2,X),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(X2,X)),X2))) = nand(nand(X2,X),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2))),
    inference(congruence,[status(thm)],[c1094]) ).

cnf(c1096,plain,
    nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(X3,X)),X3))),nand(X4,X2)) = nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2)),
    inference(congruence,[status(thm)],[c1095]) ).

cnf(c1097,plain,
    nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(X3,X)),X3))),nand(X4,X2))) = nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2))),
    inference(congruence,[status(thm)],[c1096]) ).

cnf(c1098,plain,
    nand(X,nand(nand(X2,X),X)) = nand(X2,X),
    inference(substitution,[status(thm)],[c432]) ).

cnf(c1099,plain,
    nand(X2,X) = nand(X,nand(nand(X2,X),X)),
    inference(symmetry,[status(thm)],[c1098]) ).

cnf(c1100,plain,
    nand(nand(X2,X),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2))) = nand(nand(X,nand(nand(X2,X),X)),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2))),
    inference(congruence,[status(thm)],[c1099]) ).

cnf(c1101,plain,
    nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2)) = nand(nand(nand(X,nand(nand(X3,X),X)),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2)),
    inference(congruence,[status(thm)],[c1100]) ).

cnf(c1102,plain,
    nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2))) = nand(nand(X4,X3),nand(nand(nand(X,nand(nand(X3,X),X)),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2))),
    inference(congruence,[status(thm)],[c1101]) ).

cnf(c1103,plain,
    nand(X,nand(nand(X2,X),X)) = nand(X2,X),
    inference(substitution,[status(thm)],[c432]) ).

cnf(c1104,plain,
    nand(X2,X) = nand(X,nand(nand(X2,X),X)),
    inference(symmetry,[status(thm)],[c1103]) ).

cnf(c1105,plain,
    nand(nand(X2,X),nand(X2,X)) = nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),
    inference(congruence,[status(thm)],[c1104]) ).

cnf(c1106,plain,
    nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X)) = nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X)),
    inference(congruence,[status(thm)],[c1105]) ).

cnf(c1107,plain,
    nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))) = nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),
    inference(congruence,[status(thm)],[c1106]) ).

cnf(c1108,plain,
    nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2) = nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2),
    inference(congruence,[status(thm)],[c1107]) ).

cnf(c1109,plain,
    nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2)) = nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)),
    inference(congruence,[status(thm)],[c1108]) ).

cnf(c1110,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2)) = nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2)),
    inference(congruence,[status(thm)],[c1109]) ).

cnf(c1111,plain,
    nand(nand(X,nand(nand(X2,X),X)),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2))) = nand(nand(X,nand(nand(X2,X),X)),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2))),
    inference(congruence,[status(thm)],[c1110]) ).

cnf(c1112,plain,
    nand(nand(nand(X,nand(nand(X3,X),X)),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2)) = nand(nand(nand(X,nand(nand(X3,X),X)),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2)),
    inference(congruence,[status(thm)],[c1111]) ).

cnf(c1113,plain,
    nand(nand(X4,X3),nand(nand(nand(X,nand(nand(X3,X),X)),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2))) = nand(nand(X4,X3),nand(nand(nand(X,nand(nand(X3,X),X)),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2))),
    inference(congruence,[status(thm)],[c1112]) ).

cnf(c1114,plain,
    nand(X,nand(nand(X2,X),X)) = nand(X2,X),
    inference(substitution,[status(thm)],[c432]) ).

cnf(c1115,plain,
    nand(X2,X) = nand(X,nand(nand(X2,X),X)),
    inference(symmetry,[status(thm)],[c1114]) ).

cnf(c1116,plain,
    nand(nand(X2,X),nand(X2,X)) = nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),
    inference(congruence,[status(thm)],[c1115]) ).

cnf(c1117,plain,
    nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X)) = nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X)),
    inference(congruence,[status(thm)],[c1116]) ).

cnf(c1118,plain,
    nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))) = nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),
    inference(congruence,[status(thm)],[c1117]) ).

cnf(c1119,plain,
    nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2) = nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2),
    inference(congruence,[status(thm)],[c1118]) ).

cnf(c1120,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2)) = nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)),
    inference(congruence,[status(thm)],[c1119]) ).

cnf(c1121,plain,
    nand(nand(X,nand(nand(X2,X),X)),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X2,X),nand(X2,X)),nand(X2,X))),X2))) = nand(nand(X,nand(nand(X2,X),X)),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2))),
    inference(congruence,[status(thm)],[c1120]) ).

cnf(c1122,plain,
    nand(nand(nand(X,nand(nand(X3,X),X)),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2)) = nand(nand(nand(X,nand(nand(X3,X),X)),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2)),
    inference(congruence,[status(thm)],[c1121]) ).

cnf(c1123,plain,
    nand(nand(X4,X3),nand(nand(nand(X,nand(nand(X3,X),X)),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2))) = nand(nand(X4,X3),nand(nand(nand(X,nand(nand(X3,X),X)),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2))),
    inference(congruence,[status(thm)],[c1122]) ).

cnf(c1124,plain,
    nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2) = nand(X,nand(nand(X2,X),X)),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c1125,plain,
    nand(X,nand(nand(X2,X),X)) = nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2),
    inference(symmetry,[status(thm)],[c1124]) ).

cnf(c1126,plain,
    nand(nand(X,nand(nand(X2,X),X)),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2))) = nand(nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2))),
    inference(congruence,[status(thm)],[c1125]) ).

cnf(c1127,plain,
    nand(nand(nand(X,nand(nand(X3,X),X)),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2)) = nand(nand(nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2)),
    inference(congruence,[status(thm)],[c1126]) ).

cnf(c1128,plain,
    nand(nand(X4,X3),nand(nand(nand(X,nand(nand(X3,X),X)),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2))) = nand(nand(X4,X3),nand(nand(nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2))),
    inference(congruence,[status(thm)],[c1127]) ).

cnf(c1129,plain,
    nand(nand(X4,X3),nand(nand(nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2))) = nand(nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3))),
    inference(substitution,[status(thm)],[c630]) ).

cnf(c1130,plain,
    nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2) = nand(X,nand(nand(X2,X),X)),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c1131,plain,
    nand(nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2))) = nand(nand(X,nand(nand(X2,X),X)),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2))),
    inference(congruence,[status(thm)],[c1130]) ).

cnf(c1132,plain,
    nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2) = nand(X,nand(nand(X2,X),X)),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c1133,plain,
    nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)) = nand(nand(X3,X2),nand(X,nand(nand(X2,X),X))),
    inference(congruence,[status(thm)],[c1132]) ).

cnf(c1134,plain,
    nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)) = nand(nand(nand(X3,X2),nand(X,nand(nand(X2,X),X))),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)),
    inference(congruence,[status(thm)],[c1133]) ).

cnf(c1135,plain,
    nand(nand(X,nand(nand(X2,X),X)),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2))) = nand(nand(X,nand(nand(X2,X),X)),nand(nand(nand(X3,X2),nand(X,nand(nand(X2,X),X))),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2))),
    inference(congruence,[status(thm)],[c1134]) ).

cnf(c1136,plain,
    nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2) = nand(X,nand(nand(X2,X),X)),
    inference(substitution,[status(thm)],[c7]) ).

cnf(c1137,plain,
    nand(nand(nand(X3,X2),nand(X,nand(nand(X2,X),X))),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)) = nand(nand(nand(X3,X2),nand(X,nand(nand(X2,X),X))),nand(X,nand(nand(X2,X),X))),
    inference(congruence,[status(thm)],[c1136]) ).

cnf(c1138,plain,
    nand(nand(X,nand(nand(X2,X),X)),nand(nand(nand(X3,X2),nand(X,nand(nand(X2,X),X))),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2))) = nand(nand(X,nand(nand(X2,X),X)),nand(nand(nand(X3,X2),nand(X,nand(nand(X2,X),X))),nand(X,nand(nand(X2,X),X)))),
    inference(congruence,[status(thm)],[c1137]) ).

cnf(c1139,plain,
    nand(X,nand(nand(X2,X),X)) = nand(X2,X),
    inference(substitution,[status(thm)],[c432]) ).

cnf(c1140,plain,
    nand(nand(X,nand(nand(X2,X),X)),nand(nand(nand(X3,X2),nand(X,nand(nand(X2,X),X))),nand(X,nand(nand(X2,X),X)))) = nand(nand(X2,X),nand(nand(nand(X3,X2),nand(X,nand(nand(X2,X),X))),nand(X,nand(nand(X2,X),X)))),
    inference(congruence,[status(thm)],[c1139]) ).

cnf(c1141,plain,
    nand(X,nand(nand(X2,X),X)) = nand(X2,X),
    inference(substitution,[status(thm)],[c432]) ).

cnf(c1142,plain,
    nand(nand(X3,X2),nand(X,nand(nand(X2,X),X))) = nand(nand(X3,X2),nand(X2,X)),
    inference(congruence,[status(thm)],[c1141]) ).

cnf(c1143,plain,
    nand(nand(nand(X3,X2),nand(X,nand(nand(X2,X),X))),nand(X,nand(nand(X2,X),X))) = nand(nand(nand(X3,X2),nand(X2,X)),nand(X,nand(nand(X2,X),X))),
    inference(congruence,[status(thm)],[c1142]) ).

cnf(c1144,plain,
    nand(nand(X2,X),nand(nand(nand(X3,X2),nand(X,nand(nand(X2,X),X))),nand(X,nand(nand(X2,X),X)))) = nand(nand(X2,X),nand(nand(nand(X3,X2),nand(X2,X)),nand(X,nand(nand(X2,X),X)))),
    inference(congruence,[status(thm)],[c1143]) ).

cnf(c1145,plain,
    nand(X,nand(nand(X2,X),X)) = nand(X2,X),
    inference(substitution,[status(thm)],[c432]) ).

cnf(c1146,plain,
    nand(nand(nand(X3,X2),nand(X2,X)),nand(X,nand(nand(X2,X),X))) = nand(nand(nand(X3,X2),nand(X2,X)),nand(X2,X)),
    inference(congruence,[status(thm)],[c1145]) ).

cnf(c1147,plain,
    nand(nand(X2,X),nand(nand(nand(X3,X2),nand(X2,X)),nand(X,nand(nand(X2,X),X)))) = nand(nand(X2,X),nand(nand(nand(X3,X2),nand(X2,X)),nand(X2,X))),
    inference(congruence,[status(thm)],[c1146]) ).

cnf(c1148,plain,
    nand(nand(X2,X),nand(nand(nand(X3,X2),nand(X2,X)),nand(X2,X))) = nand(nand(X2,X),nand(X3,X2)),
    inference(substitution,[status(thm)],[c239]) ).

cnf(c1149,plain,
    nand(nand(X3,X2),nand(X2,X)) = nand(nand(X2,X),nand(X3,X2)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c1150,plain,
    nand(nand(X2,X),nand(X3,X2)) = nand(nand(X3,X2),nand(X2,X)),
    inference(symmetry,[status(thm)],[c1149]) ).

cnf(c1151,plain,
    nand(nand(X2,X),nand(nand(nand(X3,X2),nand(X2,X)),nand(X2,X))) = nand(nand(X3,X2),nand(X2,X)),
    inference(transitivity,[status(thm)],[c1148,c1150]) ).

cnf(c1152,plain,
    nand(nand(X2,X),nand(nand(nand(X3,X2),nand(X2,X)),nand(X,nand(nand(X2,X),X)))) = nand(nand(X3,X2),nand(X2,X)),
    inference(transitivity,[status(thm)],[c1147,c1151]) ).

cnf(c1153,plain,
    nand(nand(X2,X),nand(nand(nand(X3,X2),nand(X,nand(nand(X2,X),X))),nand(X,nand(nand(X2,X),X)))) = nand(nand(X3,X2),nand(X2,X)),
    inference(transitivity,[status(thm)],[c1144,c1152]) ).

cnf(c1154,plain,
    nand(nand(X,nand(nand(X2,X),X)),nand(nand(nand(X3,X2),nand(X,nand(nand(X2,X),X))),nand(X,nand(nand(X2,X),X)))) = nand(nand(X3,X2),nand(X2,X)),
    inference(transitivity,[status(thm)],[c1140,c1153]) ).

cnf(c1155,plain,
    nand(nand(X,nand(nand(X2,X),X)),nand(nand(nand(X3,X2),nand(X,nand(nand(X2,X),X))),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2))) = nand(nand(X3,X2),nand(X2,X)),
    inference(transitivity,[status(thm)],[c1138,c1154]) ).

cnf(c1156,plain,
    nand(nand(X,nand(nand(X2,X),X)),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2))) = nand(nand(X3,X2),nand(X2,X)),
    inference(transitivity,[status(thm)],[c1135,c1155]) ).

cnf(c1157,plain,
    nand(nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2),nand(nand(nand(X3,X2),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2)),nand(nand(nand(X2,X),nand(nand(nand(X,nand(nand(X2,X),X)),nand(X2,X)),nand(X2,X))),X2))) = nand(nand(X3,X2),nand(X2,X)),
    inference(transitivity,[status(thm)],[c1131,c1156]) ).

cnf(c1158,plain,
    nand(nand(X4,X3),nand(nand(nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2))) = nand(nand(X4,X3),nand(X3,X)),
    inference(transitivity,[status(thm)],[c1129,c1157]) ).

cnf(c1159,plain,
    nand(nand(X4,X3),nand(nand(nand(X,nand(nand(X3,X),X)),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2))) = nand(nand(X4,X3),nand(X3,X)),
    inference(transitivity,[status(thm)],[c1128,c1158]) ).

cnf(c1160,plain,
    nand(nand(X4,X3),nand(nand(nand(X,nand(nand(X3,X),X)),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X,nand(nand(X3,X),X)),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2))) = nand(nand(X4,X3),nand(X3,X)),
    inference(transitivity,[status(thm)],[c1123,c1159]) ).

cnf(c1161,plain,
    nand(nand(X4,X3),nand(nand(nand(X,nand(nand(X3,X),X)),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2))) = nand(nand(X4,X3),nand(X3,X)),
    inference(transitivity,[status(thm)],[c1113,c1160]) ).

cnf(c1162,plain,
    nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3))),nand(X4,X2))) = nand(nand(X4,X3),nand(X3,X)),
    inference(transitivity,[status(thm)],[c1102,c1161]) ).

cnf(c1163,plain,
    nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X3,X),nand(X3,X)),nand(X3,X))),X3)),nand(nand(nand(X3,X),nand(X3,X)),X3))),nand(X4,X2))) = nand(nand(X4,X3),nand(X3,X)),
    inference(transitivity,[status(thm)],[c1097,c1162]) ).

cnf(c1164,plain,
    nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(X3,X)),X3)),nand(nand(nand(X3,X),nand(X3,X)),X3))),nand(X4,X2))) = nand(nand(X4,X3),nand(X3,X)),
    inference(transitivity,[status(thm)],[c1090,c1163]) ).

cnf(c1165,plain,
    nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(nand(nand(X3,X),nand(X3,X)),X3)),nand(X3,X))),nand(X4,X2))) = nand(nand(X4,X3),nand(X3,X)),
    inference(transitivity,[status(thm)],[c1082,c1164]) ).

cnf(c1166,plain,
    nand(nand(X4,X3),nand(nand(nand(X3,X),nand(nand(nand(X4,X3),nand(X3,X)),nand(X3,X))),nand(X4,X2))) = nand(nand(X4,X3),nand(X3,X)),
    inference(transitivity,[status(thm)],[c1077,c1165]) ).

cnf(c1167,plain,
    nand(nand(X4,X3),nand(nand(nand(X3,X),nand(X4,X3)),nand(X4,X2))) = nand(nand(X4,X3),nand(X3,X)),
    inference(transitivity,[status(thm)],[c1071,c1166]) ).

cnf(c1168,plain,
    nand(nand(X4,X3),nand(nand(X4,X2),nand(nand(X3,X),nand(X4,X3)))) = nand(nand(X4,X3),nand(X3,X)),
    inference(transitivity,[status(thm)],[c1067,c1167]) ).

cnf(c1169,plain,
    nand(nand(X4,X3),nand(nand(X4,X2),nand(nand(X4,X3),nand(X3,X)))) = nand(nand(X4,X3),nand(X3,X)),
    inference(transitivity,[status(thm)],[c1065,c1168]) ).

cnf(c1170,plain,
    nand(nand(X4,X2),nand(nand(X4,nand(X3,nand(X4,X2))),nand(nand(X4,X2),nand(X2,X)))) = nand(nand(X4,X2),nand(X2,X)),
    inference(substitution,[status(thm)],[c1169]) ).

cnf(c1171,plain,
    nand(nand(X4,X2),nand(X2,X)) = nand(nand(X4,X2),nand(nand(X4,nand(X3,nand(X4,X2))),nand(nand(X4,X2),nand(X2,X)))),
    inference(symmetry,[status(thm)],[c1170]) ).

cnf(c1172,plain,
    nand(nand(nand(X4,X2),nand(X4,nand(X3,nand(X4,X2)))),nand(nand(X4,X2),nand(X2,X))) = nand(nand(nand(X4,X2),nand(X4,nand(X3,nand(X4,X2)))),nand(nand(X4,X2),nand(nand(X4,nand(X3,nand(X4,X2))),nand(nand(X4,X2),nand(X2,X))))),
    inference(congruence,[status(thm)],[c1171]) ).

cnf(c1173,plain,
    nand(nand(nand(X4,X2),nand(X4,nand(X3,nand(X4,X2)))),nand(nand(X4,X2),nand(nand(X4,nand(X3,nand(X4,X2))),nand(nand(X4,X2),nand(X2,X))))) = nand(X4,X2),
    inference(substitution,[status(thm)],[c514]) ).

cnf(c1174,plain,
    nand(nand(nand(X4,X2),nand(X4,nand(X3,nand(X4,X2)))),nand(nand(X4,X2),nand(X2,X))) = nand(X4,X2),
    inference(transitivity,[status(thm)],[c1172,c1173]) ).

cnf(c1175,plain,
    nand(nand(nand(X4,nand(X3,nand(X4,X2))),nand(X4,nand(X3,nand(X4,X2)))),nand(nand(X4,X2),nand(X2,X))) = nand(X4,X2),
    inference(transitivity,[status(thm)],[c1062,c1174]) ).

cnf(c1176,plain,
    nand(nand(nand(X4,nand(X,nand(X4,X3))),nand(X4,nand(X,nand(X4,X3)))),nand(nand(X4,X3),nand(X3,X2))) = nand(X4,X3),
    inference(substitution,[status(thm)],[c1175]) ).

cnf(c1177,plain,
    nand(X4,X3) = nand(nand(nand(X4,nand(X,nand(X4,X3))),nand(X4,nand(X,nand(X4,X3)))),nand(nand(X4,X3),nand(X3,X2))),
    inference(symmetry,[status(thm)],[c1176]) ).

cnf(c1178,plain,
    nand(nand(nand(X3,X2),nand(nand(X4,nand(X,nand(X4,X3))),nand(X4,nand(X,nand(X4,X3))))),nand(X4,X3)) = nand(nand(nand(X3,X2),nand(nand(X4,nand(X,nand(X4,X3))),nand(X4,nand(X,nand(X4,X3))))),nand(nand(nand(X4,nand(X,nand(X4,X3))),nand(X4,nand(X,nand(X4,X3)))),nand(nand(X4,X3),nand(X3,X2)))),
    inference(congruence,[status(thm)],[c1177]) ).

cnf(c1179,plain,
    nand(nand(nand(X3,X2),nand(nand(X4,nand(X,nand(X4,X3))),nand(X4,nand(X,nand(X4,X3))))),nand(nand(nand(X4,nand(X,nand(X4,X3))),nand(X4,nand(X,nand(X4,X3)))),nand(nand(X4,X3),nand(X3,X2)))) = nand(nand(X4,nand(X,nand(X4,X3))),nand(X4,nand(X,nand(X4,X3)))),
    inference(substitution,[status(thm)],[c281]) ).

cnf(c1180,plain,
    nand(nand(nand(X3,X2),nand(nand(X4,nand(X,nand(X4,X3))),nand(X4,nand(X,nand(X4,X3))))),nand(X4,X3)) = nand(nand(X4,nand(X,nand(X4,X3))),nand(X4,nand(X,nand(X4,X3)))),
    inference(transitivity,[status(thm)],[c1178,c1179]) ).

cnf(c1181,plain,
    nand(nand(X4,X3),nand(nand(X3,X2),nand(nand(X4,nand(X,nand(X4,X3))),nand(X4,nand(X,nand(X4,X3)))))) = nand(nand(X4,nand(X,nand(X4,X3))),nand(X4,nand(X,nand(X4,X3)))),
    inference(transitivity,[status(thm)],[c1045,c1180]) ).

cnf(c1182,plain,
    nand(nand(X4,X2),nand(nand(X2,X),nand(nand(X4,nand(X3,nand(X4,X2))),nand(X4,nand(X3,nand(X4,X2)))))) = nand(nand(X4,nand(X3,nand(X4,X2))),nand(X4,nand(X3,nand(X4,X2)))),
    inference(substitution,[status(thm)],[c1181]) ).

cnf(c1183,plain,
    nand(nand(X4,nand(X3,nand(X4,X2))),nand(X4,nand(X3,nand(X4,X2)))) = nand(nand(X4,X2),nand(nand(X2,X),nand(nand(X4,nand(X3,nand(X4,X2))),nand(X4,nand(X3,nand(X4,X2)))))),
    inference(symmetry,[status(thm)],[c1182]) ).

cnf(c1184,plain,
    nand(nand(X5,nand(X4,X2)),nand(nand(X4,nand(X3,nand(X4,X2))),nand(X4,nand(X3,nand(X4,X2))))) = nand(nand(X5,nand(X4,X2)),nand(nand(X4,X2),nand(nand(X2,X),nand(nand(X4,nand(X3,nand(X4,X2))),nand(X4,nand(X3,nand(X4,X2))))))),
    inference(congruence,[status(thm)],[c1183]) ).

cnf(c1185,plain,
    nand(nand(X5,nand(X4,X2)),nand(nand(X5,nand(X4,X2)),nand(nand(X4,nand(X3,nand(X4,X2))),nand(X4,nand(X3,nand(X4,X2)))))) = nand(nand(X5,nand(X4,X2)),nand(nand(X5,nand(X4,X2)),nand(nand(X4,X2),nand(nand(X2,X),nand(nand(X4,nand(X3,nand(X4,X2))),nand(X4,nand(X3,nand(X4,X2)))))))),
    inference(congruence,[status(thm)],[c1184]) ).

cnf(c1186,plain,
    nand(X5,nand(nand(X5,nand(X4,X2)),nand(nand(X5,nand(X4,X2)),nand(nand(X4,nand(X3,nand(X4,X2))),nand(X4,nand(X3,nand(X4,X2))))))) = nand(X5,nand(nand(X5,nand(X4,X2)),nand(nand(X5,nand(X4,X2)),nand(nand(X4,X2),nand(nand(X2,X),nand(nand(X4,nand(X3,nand(X4,X2))),nand(X4,nand(X3,nand(X4,X2))))))))),
    inference(congruence,[status(thm)],[c1185]) ).

cnf(c1187,plain,
    nand(X5,nand(nand(X5,nand(X4,X2)),nand(nand(X5,nand(X4,X2)),nand(nand(X4,X2),nand(nand(X2,X),nand(nand(X4,nand(X3,nand(X4,X2))),nand(X4,nand(X3,nand(X4,X2))))))))) = nand(X5,X5),
    inference(substitution,[status(thm)],[c889]) ).

cnf(c1188,plain,
    nand(X4,nand(nand(X4,nand(X3,X)),nand(nand(X4,nand(X3,X)),nand(nand(X3,nand(X2,nand(X3,X))),nand(X3,nand(X2,nand(X3,X))))))) = nand(X4,X4),
    inference(transitivity,[status(thm)],[c1186,c1187]) ).

cnf(c1189,plain,
    nand(X4,nand(nand(X4,nand(X3,X)),nand(X3,nand(X2,nand(X3,X))))) = nand(X4,X4),
    inference(transitivity,[status(thm)],[c1044,c1188]) ).

cnf(c1190,plain,
    nand(X4,nand(nand(X3,nand(X2,nand(X3,X))),nand(X4,nand(X3,X)))) = nand(X4,X4),
    inference(transitivity,[status(thm)],[c1041,c1189]) ).

cnf(c1191,plain,
    nand(X,nand(nand(X4,nand(X3,nand(X4,X2))),nand(X,nand(X4,X2)))) = nand(X,X),
    inference(substitution,[status(thm)],[c1190]) ).

cnf(c1192,plain,
    nand(nand(X4,nand(X3,nand(X4,X2))),nand(X,nand(nand(X4,nand(X3,nand(X4,X2))),nand(X,nand(X4,X2))))) = nand(nand(X4,nand(X3,nand(X4,X2))),nand(X,X)),
    inference(congruence,[status(thm)],[c1191]) ).

cnf(c1193,plain,
    nand(nand(X4,nand(X3,nand(X4,X2))),nand(X,nand(X4,X2))) = nand(nand(X4,nand(X3,nand(X4,X2))),nand(X,X)),
    inference(transitivity,[status(thm)],[c1039,c1192]) ).

cnf(c1194,plain,
    nand(nand(X2,nand(X3,nand(X2,X))),nand(nand(X3,nand(X2,X)),nand(X2,X))) = nand(nand(X2,nand(X3,nand(X2,X))),nand(nand(X3,nand(X2,X)),nand(X3,nand(X2,X)))),
    inference(substitution,[status(thm)],[c1193]) ).

cnf(c1195,plain,
    nand(nand(nand(nand(nand(X,X3),X3),X2),nand(nand(nand(X,X3),X3),X2)),nand(nand(X2,nand(X3,nand(X2,X))),nand(nand(X3,nand(X2,X)),nand(X2,X)))) = nand(nand(nand(nand(nand(X,X3),X3),X2),nand(nand(nand(X,X3),X3),X2)),nand(nand(X2,nand(X3,nand(X2,X))),nand(nand(X3,nand(X2,X)),nand(X3,nand(X2,X))))),
    inference(congruence,[status(thm)],[c1194]) ).

cnf(c1196,plain,
    nand(nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2)),nand(nand(X2,nand(X3,nand(X2,X4))),nand(X,nand(X3,nand(X2,X4))))) = nand(nand(nand(X2,nand(X3,nand(X2,X4))),nand(X,nand(X3,nand(X2,X4)))),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2))),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c1197,plain,
    nand(nand(X,nand(X3,nand(X4,X2))),nand(nand(nand(nand(X2,X3),X3),X4),nand(nand(nand(X2,X3),X3),X4))) = nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(nand(nand(X2,X3),X3),X4)),nand(X,nand(X3,nand(X4,X2)))),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c1198,plain,
    nand(nand(X4,nand(X3,nand(X4,X2))),nand(nand(X,nand(X3,nand(X4,X2))),nand(nand(nand(nand(X2,X3),X3),X4),nand(nand(nand(X2,X3),X3),X4)))) = nand(nand(X4,nand(X3,nand(X4,X2))),nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(nand(nand(X2,X3),X3),X4)),nand(X,nand(X3,nand(X4,X2))))),
    inference(congruence,[status(thm)],[c1197]) ).

cnf(c1199,plain,
    nand(nand(X4,nand(X3,nand(X4,X2))),nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(nand(nand(X2,X3),X3),X4)),nand(X,nand(X3,nand(X4,X2))))) = nand(nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(nand(nand(X2,X3),X3),X4)),nand(X,nand(X3,nand(X4,X2)))),nand(X4,nand(X3,nand(X4,X2)))),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c1200,plain,
    nand(X4,nand(nand(nand(nand(X3,X2),X2),X4),nand(X,nand(X2,nand(X4,X3))))) = nand(nand(nand(nand(nand(X3,X2),X2),X4),nand(X,nand(X2,nand(X4,X3)))),X4),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c1201,plain,
    nand(nand(nand(nand(X2,X),X),X3),nand(X3,X3)) = X3,
    inference(substitution,[status(thm)],[c479]) ).

cnf(c1202,plain,
    X3 = nand(nand(nand(nand(X2,X),X),X3),nand(X3,X3)),
    inference(symmetry,[status(thm)],[c1201]) ).

cnf(c1203,plain,
    nand(nand(nand(nand(nand(X3,X2),X2),X4),nand(X,nand(X2,nand(X4,X3)))),X4) = nand(nand(nand(nand(nand(X3,X2),X2),X4),nand(X,nand(X2,nand(X4,X3)))),nand(nand(nand(nand(X3,X2),X2),X4),nand(X4,X4))),
    inference(congruence,[status(thm)],[c1202]) ).

cnf(c1204,plain,
    nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(nand(X2,X),X),X3),X)) = nand(nand(nand(nand(X2,X),X),X3),nand(X,nand(X3,X2))),
    inference(substitution,[status(thm)],[c898]) ).

cnf(c1205,plain,
    nand(nand(nand(nand(X2,X),X),X3),nand(X,nand(X3,X2))) = nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(nand(X2,X),X),X3),X)),
    inference(symmetry,[status(thm)],[c1204]) ).

cnf(c1206,plain,
    nand(X3,nand(nand(nand(nand(X2,X),X),X3),nand(X,nand(X3,X2)))) = nand(X3,nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(nand(X2,X),X),X3),X))),
    inference(congruence,[status(thm)],[c1205]) ).

cnf(c1207,plain,
    nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(nand(X2,X),X),X3),X)) = nand(nand(nand(nand(nand(X2,X),X),X3),X),nand(nand(nand(X2,X),X),X3)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c1208,plain,
    nand(X3,nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(nand(X2,X),X),X3),X))) = nand(X3,nand(nand(nand(nand(nand(X2,X),X),X3),X),nand(nand(nand(X2,X),X),X3))),
    inference(congruence,[status(thm)],[c1207]) ).

cnf(c1209,plain,
    nand(X3,nand(nand(nand(X2,X),X3),X)) = nand(nand(nand(nand(X2,X),X3),X),X3),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c1210,plain,
    nand(nand(nand(X2,X),X3),nand(X3,X3)) = X3,
    inference(substitution,[status(thm)],[c479]) ).

cnf(c1211,plain,
    X3 = nand(nand(nand(X2,X),X3),nand(X3,X3)),
    inference(symmetry,[status(thm)],[c1210]) ).

cnf(c1212,plain,
    nand(nand(nand(nand(X2,X),X3),X),X3) = nand(nand(nand(nand(X2,X),X3),X),nand(nand(nand(X2,X),X3),nand(X3,X3))),
    inference(congruence,[status(thm)],[c1211]) ).

cnf(c1213,plain,
    nand(nand(X,X2),nand(nand(X,X2),nand(nand(X,X2),X))) = nand(nand(X,X2),X),
    inference(substitution,[status(thm)],[c732]) ).

cnf(c1214,plain,
    nand(nand(X,X2),X) = nand(nand(X,X2),nand(nand(X,X2),nand(nand(X,X2),X))),
    inference(symmetry,[status(thm)],[c1213]) ).

cnf(c1215,plain,
    nand(X2,nand(nand(X,X2),X)) = nand(X2,nand(nand(X,X2),nand(nand(X,X2),nand(nand(X,X2),X)))),
    inference(congruence,[status(thm)],[c1214]) ).

cnf(c1216,plain,
    nand(nand(X2,X3),nand(nand(X2,X3),nand(X,X2))) = nand(nand(nand(X2,X3),nand(X,X2)),nand(X2,X3)),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c1217,plain,
    nand(X3,nand(nand(X2,X3),nand(nand(X2,X3),nand(X,X2)))) = nand(X3,nand(nand(nand(X2,X3),nand(X,X2)),nand(X2,X3))),
    inference(congruence,[status(thm)],[c1216]) ).

cnf(c1218,plain,
    nand(X2,X3) = nand(X3,nand(nand(X2,X3),nand(X,X2))),
    inference(symmetry,[status(thm)],[c759]) ).

cnf(c1219,plain,
    nand(nand(nand(X2,X3),nand(X,X2)),nand(X2,X3)) = nand(nand(nand(X2,X3),nand(X,X2)),nand(X3,nand(nand(X2,X3),nand(X,X2)))),
    inference(congruence,[status(thm)],[c1218]) ).

cnf(c1220,plain,
    nand(X3,nand(nand(nand(X2,X3),nand(X,X2)),nand(X2,X3))) = nand(X3,nand(nand(nand(X2,X3),nand(X,X2)),nand(X3,nand(nand(X2,X3),nand(X,X2))))),
    inference(congruence,[status(thm)],[c1219]) ).

cnf(c1221,plain,
    nand(X3,nand(nand(nand(X2,X3),nand(X,X2)),nand(X3,nand(nand(X2,X3),nand(X,X2))))) = nand(X3,X3),
    inference(substitution,[status(thm)],[c332]) ).

cnf(c1222,plain,
    nand(X3,nand(nand(nand(X2,X3),nand(X,X2)),nand(X2,X3))) = nand(X3,X3),
    inference(transitivity,[status(thm)],[c1220,c1221]) ).

cnf(c1223,plain,
    nand(X3,nand(nand(X2,X3),nand(nand(X2,X3),nand(X,X2)))) = nand(X3,X3),
    inference(transitivity,[status(thm)],[c1217,c1222]) ).

cnf(c1224,plain,
    nand(X2,nand(nand(X,X2),nand(nand(X,X2),nand(nand(X,X2),X)))) = nand(X2,X2),
    inference(substitution,[status(thm)],[c1223]) ).

cnf(c1225,plain,
    nand(X2,nand(nand(X,X2),X)) = nand(X2,X2),
    inference(transitivity,[status(thm)],[c1215,c1224]) ).

cnf(c1226,plain,
    nand(X3,nand(nand(nand(X2,X),X3),nand(X2,X))) = nand(X3,X3),
    inference(substitution,[status(thm)],[c1225]) ).

cnf(c1227,plain,
    nand(X3,X3) = nand(X3,nand(nand(nand(X2,X),X3),nand(X2,X))),
    inference(symmetry,[status(thm)],[c1226]) ).

cnf(c1228,plain,
    nand(nand(nand(X2,X),X3),nand(X3,X3)) = nand(nand(nand(X2,X),X3),nand(X3,nand(nand(nand(X2,X),X3),nand(X2,X)))),
    inference(congruence,[status(thm)],[c1227]) ).

cnf(c1229,plain,
    nand(nand(nand(nand(X2,X),X3),X),nand(nand(nand(X2,X),X3),nand(X3,X3))) = nand(nand(nand(nand(X2,X),X3),X),nand(nand(nand(X2,X),X3),nand(X3,nand(nand(nand(X2,X),X3),nand(X2,X))))),
    inference(congruence,[status(thm)],[c1228]) ).

cnf(c1230,plain,
    nand(nand(nand(nand(X2,X),X3),X),nand(nand(nand(X2,X),X3),nand(X3,nand(nand(nand(X2,X),X3),nand(X2,X))))) = nand(nand(X2,X),X3),
    inference(substitution,[status(thm)],[c778]) ).

cnf(c1231,plain,
    nand(nand(nand(nand(X2,X),X3),X),nand(nand(nand(X2,X),X3),nand(X3,X3))) = nand(nand(X2,X),X3),
    inference(transitivity,[status(thm)],[c1229,c1230]) ).

cnf(c1232,plain,
    nand(nand(nand(nand(X2,X),X3),X),X3) = nand(nand(X2,X),X3),
    inference(transitivity,[status(thm)],[c1212,c1231]) ).

cnf(c1233,plain,
    nand(X3,nand(nand(nand(X2,X),X3),X)) = nand(nand(X2,X),X3),
    inference(transitivity,[status(thm)],[c1209,c1232]) ).

cnf(c1234,plain,
    nand(X3,nand(nand(nand(nand(X2,X),X),X3),X)) = nand(nand(nand(X2,X),X),X3),
    inference(substitution,[status(thm)],[c1233]) ).

cnf(c1235,plain,
    nand(nand(nand(X2,X),X),X3) = nand(X3,nand(nand(nand(nand(X2,X),X),X3),X)),
    inference(symmetry,[status(thm)],[c1234]) ).

cnf(c1236,plain,
    nand(nand(nand(nand(nand(X2,X),X),X3),X),nand(nand(nand(X2,X),X),X3)) = nand(nand(nand(nand(nand(X2,X),X),X3),X),nand(X3,nand(nand(nand(nand(X2,X),X),X3),X))),
    inference(congruence,[status(thm)],[c1235]) ).

cnf(c1237,plain,
    nand(X3,nand(nand(nand(nand(nand(X2,X),X),X3),X),nand(nand(nand(X2,X),X),X3))) = nand(X3,nand(nand(nand(nand(nand(X2,X),X),X3),X),nand(X3,nand(nand(nand(nand(X2,X),X),X3),X)))),
    inference(congruence,[status(thm)],[c1236]) ).

cnf(c1238,plain,
    nand(X3,nand(nand(nand(nand(nand(X2,X),X),X3),X),nand(X3,nand(nand(nand(nand(X2,X),X),X3),X)))) = nand(X3,X3),
    inference(substitution,[status(thm)],[c332]) ).

cnf(c1239,plain,
    nand(X3,nand(nand(nand(nand(nand(X2,X),X),X3),X),nand(nand(nand(X2,X),X),X3))) = nand(X3,X3),
    inference(transitivity,[status(thm)],[c1237,c1238]) ).

cnf(c1240,plain,
    nand(X3,nand(nand(nand(nand(X2,X),X),X3),nand(nand(nand(nand(X2,X),X),X3),X))) = nand(X3,X3),
    inference(transitivity,[status(thm)],[c1208,c1239]) ).

cnf(c1241,plain,
    nand(X3,nand(nand(nand(nand(X2,X),X),X3),nand(X,nand(X3,X2)))) = nand(X3,X3),
    inference(transitivity,[status(thm)],[c1206,c1240]) ).

cnf(c1242,plain,
    nand(X3,X3) = nand(X3,nand(nand(nand(nand(X2,X),X),X3),nand(X,nand(X3,X2)))),
    inference(symmetry,[status(thm)],[c1241]) ).

cnf(c1243,plain,
    nand(nand(nand(nand(X2,X),X),X3),nand(X3,X3)) = nand(nand(nand(nand(X2,X),X),X3),nand(X3,nand(nand(nand(nand(X2,X),X),X3),nand(X,nand(X3,X2))))),
    inference(congruence,[status(thm)],[c1242]) ).

cnf(c1244,plain,
    nand(nand(nand(nand(nand(X3,X2),X2),X4),nand(X,nand(X2,nand(X4,X3)))),nand(nand(nand(nand(X3,X2),X2),X4),nand(X4,X4))) = nand(nand(nand(nand(nand(X3,X2),X2),X4),nand(X,nand(X2,nand(X4,X3)))),nand(nand(nand(nand(X3,X2),X2),X4),nand(X4,nand(nand(nand(nand(X3,X2),X2),X4),nand(X2,nand(X4,X3)))))),
    inference(congruence,[status(thm)],[c1243]) ).

cnf(c1245,plain,
    nand(nand(nand(nand(nand(X3,X2),X2),X4),nand(X,nand(X2,nand(X4,X3)))),nand(nand(nand(nand(X3,X2),X2),X4),nand(X4,nand(nand(nand(nand(X3,X2),X2),X4),nand(X2,nand(X4,X3)))))) = nand(nand(nand(X3,X2),X2),X4),
    inference(substitution,[status(thm)],[c921]) ).

cnf(c1246,plain,
    nand(nand(nand(nand(nand(X3,X2),X2),X4),nand(X,nand(X2,nand(X4,X3)))),nand(nand(nand(nand(X3,X2),X2),X4),nand(X4,X4))) = nand(nand(nand(X3,X2),X2),X4),
    inference(transitivity,[status(thm)],[c1244,c1245]) ).

cnf(c1247,plain,
    nand(nand(nand(nand(nand(X3,X2),X2),X4),nand(X,nand(X2,nand(X4,X3)))),X4) = nand(nand(nand(X3,X2),X2),X4),
    inference(transitivity,[status(thm)],[c1203,c1246]) ).

cnf(c1248,plain,
    nand(X4,nand(nand(nand(nand(X3,X2),X2),X4),nand(X,nand(X2,nand(X4,X3))))) = nand(nand(nand(X3,X2),X2),X4),
    inference(transitivity,[status(thm)],[c1200,c1247]) ).

cnf(c1249,plain,
    nand(X,nand(nand(nand(nand(X3,X2),X2),X),nand(X,nand(X2,nand(X,X3))))) = nand(nand(nand(X3,X2),X2),X),
    inference(substitution,[status(thm)],[c1248]) ).

cnf(c1250,plain,
    nand(nand(nand(X3,X2),X2),X) = nand(X,nand(nand(nand(nand(X3,X2),X2),X),nand(X,nand(X2,nand(X,X3))))),
    inference(symmetry,[status(thm)],[c1249]) ).

cnf(c1251,plain,
    nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X3,X2),X2),X)) = nand(nand(nand(nand(X3,X2),X2),X),nand(X,nand(nand(nand(nand(X3,X2),X2),X),nand(X,nand(X2,nand(X,X3)))))),
    inference(congruence,[status(thm)],[c1250]) ).

cnf(c1252,plain,
    nand(nand(nand(nand(X3,X2),X2),X),nand(X,nand(nand(nand(nand(X3,X2),X2),X),nand(X,nand(X2,nand(X,X3)))))) = nand(nand(nand(nand(X3,X2),X2),X),nand(X,nand(X2,nand(X,X3)))),
    inference(substitution,[status(thm)],[c325]) ).

cnf(c1253,plain,
    nand(nand(nand(nand(X3,X2),X2),X),nand(nand(nand(X3,X2),X2),X)) = nand(nand(nand(nand(X3,X2),X2),X),nand(X,nand(X2,nand(X,X3)))),
    inference(transitivity,[status(thm)],[c1251,c1252]) ).

cnf(c1254,plain,
    nand(nand(nand(nand(X,X2),X2),X3),nand(nand(nand(X,X2),X2),X3)) = nand(nand(nand(nand(X,X2),X2),X3),nand(X3,nand(X2,nand(X3,X)))),
    inference(substitution,[status(thm)],[c1253]) ).

cnf(c1255,plain,
    nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(nand(nand(X2,X3),X3),X4)),nand(X,nand(X3,nand(X4,X2)))) = nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(X4,nand(X3,nand(X4,X2)))),nand(X,nand(X3,nand(X4,X2)))),
    inference(congruence,[status(thm)],[c1254]) ).

cnf(c1256,plain,
    nand(nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(nand(nand(X2,X3),X3),X4)),nand(X,nand(X3,nand(X4,X2)))),nand(X4,nand(X3,nand(X4,X2)))) = nand(nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(X4,nand(X3,nand(X4,X2)))),nand(X,nand(X3,nand(X4,X2)))),nand(X4,nand(X3,nand(X4,X2)))),
    inference(congruence,[status(thm)],[c1255]) ).

cnf(c1257,plain,
    nand(nand(nand(nand(nand(X,X2),X2),X3),nand(X3,nand(X2,nand(X3,X)))),nand(nand(X3,nand(X2,nand(X3,X))),nand(nand(nand(nand(nand(X,X2),X2),X3),nand(X3,nand(X2,nand(X3,X)))),nand(X2,nand(X3,X))))) = nand(X3,nand(X2,nand(X3,X))),
    inference(substitution,[status(thm)],[c983]) ).

cnf(c1258,plain,
    nand(X3,nand(X2,nand(X3,X))) = nand(nand(nand(nand(nand(X,X2),X2),X3),nand(X3,nand(X2,nand(X3,X)))),nand(nand(X3,nand(X2,nand(X3,X))),nand(nand(nand(nand(nand(X,X2),X2),X3),nand(X3,nand(X2,nand(X3,X)))),nand(X2,nand(X3,X))))),
    inference(symmetry,[status(thm)],[c1257]) ).

cnf(c1259,plain,
    nand(nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(X4,nand(X3,nand(X4,X2)))),nand(X,nand(X3,nand(X4,X2)))),nand(X4,nand(X3,nand(X4,X2)))) = nand(nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(X4,nand(X3,nand(X4,X2)))),nand(X,nand(X3,nand(X4,X2)))),nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(X4,nand(X3,nand(X4,X2)))),nand(nand(X4,nand(X3,nand(X4,X2))),nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(X4,nand(X3,nand(X4,X2)))),nand(X3,nand(X4,X2)))))),
    inference(congruence,[status(thm)],[c1258]) ).

cnf(c1260,plain,
    nand(nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(X4,nand(X3,nand(X4,X2)))),nand(X,nand(X3,nand(X4,X2)))),nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(X4,nand(X3,nand(X4,X2)))),nand(nand(X4,nand(X3,nand(X4,X2))),nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(X4,nand(X3,nand(X4,X2)))),nand(X3,nand(X4,X2)))))) = nand(nand(nand(nand(X2,X3),X3),X4),nand(X4,nand(X3,nand(X4,X2)))),
    inference(substitution,[status(thm)],[c921]) ).

cnf(c1261,plain,
    nand(nand(nand(nand(X,X2),X2),X3),nand(nand(nand(X,X2),X2),X3)) = nand(nand(nand(nand(X,X2),X2),X3),nand(X3,nand(X2,nand(X3,X)))),
    inference(substitution,[status(thm)],[c1253]) ).

cnf(c1262,plain,
    nand(nand(nand(nand(X,X2),X2),X3),nand(X3,nand(X2,nand(X3,X)))) = nand(nand(nand(nand(X,X2),X2),X3),nand(nand(nand(X,X2),X2),X3)),
    inference(symmetry,[status(thm)],[c1261]) ).

cnf(c1263,plain,
    nand(nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(X4,nand(X3,nand(X4,X2)))),nand(X,nand(X3,nand(X4,X2)))),nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(X4,nand(X3,nand(X4,X2)))),nand(nand(X4,nand(X3,nand(X4,X2))),nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(X4,nand(X3,nand(X4,X2)))),nand(X3,nand(X4,X2)))))) = nand(nand(nand(nand(X2,X3),X3),X4),nand(nand(nand(X2,X3),X3),X4)),
    inference(transitivity,[status(thm)],[c1260,c1262]) ).

cnf(c1264,plain,
    nand(nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(X4,nand(X3,nand(X4,X2)))),nand(X,nand(X3,nand(X4,X2)))),nand(X4,nand(X3,nand(X4,X2)))) = nand(nand(nand(nand(X2,X3),X3),X4),nand(nand(nand(X2,X3),X3),X4)),
    inference(transitivity,[status(thm)],[c1259,c1263]) ).

cnf(c1265,plain,
    nand(nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(nand(nand(X2,X3),X3),X4)),nand(X,nand(X3,nand(X4,X2)))),nand(X4,nand(X3,nand(X4,X2)))) = nand(nand(nand(nand(X2,X3),X3),X4),nand(nand(nand(X2,X3),X3),X4)),
    inference(transitivity,[status(thm)],[c1256,c1264]) ).

cnf(c1266,plain,
    nand(nand(X4,nand(X3,nand(X4,X2))),nand(nand(nand(nand(nand(X2,X3),X3),X4),nand(nand(nand(X2,X3),X3),X4)),nand(X,nand(X3,nand(X4,X2))))) = nand(nand(nand(nand(X2,X3),X3),X4),nand(nand(nand(X2,X3),X3),X4)),
    inference(transitivity,[status(thm)],[c1199,c1265]) ).

cnf(c1267,plain,
    nand(nand(X4,nand(X3,nand(X4,X2))),nand(nand(X,nand(X3,nand(X4,X2))),nand(nand(nand(nand(X2,X3),X3),X4),nand(nand(nand(X2,X3),X3),X4)))) = nand(nand(nand(nand(X2,X3),X3),X4),nand(nand(nand(X2,X3),X3),X4)),
    inference(transitivity,[status(thm)],[c1198,c1266]) ).

cnf(c1268,plain,
    nand(nand(X2,nand(X3,nand(X2,X4))),nand(nand(X,nand(X3,nand(X2,X4))),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2)))) = nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2)),
    inference(substitution,[status(thm)],[c1267]) ).

cnf(c1269,plain,
    nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2)) = nand(nand(X2,nand(X3,nand(X2,X4))),nand(nand(X,nand(X3,nand(X2,X4))),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2)))),
    inference(symmetry,[status(thm)],[c1268]) ).

cnf(c1270,plain,
    nand(nand(nand(X2,nand(X3,nand(X2,X4))),nand(X,nand(X3,nand(X2,X4)))),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2))) = nand(nand(nand(X2,nand(X3,nand(X2,X4))),nand(X,nand(X3,nand(X2,X4)))),nand(nand(X2,nand(X3,nand(X2,X4))),nand(nand(X,nand(X3,nand(X2,X4))),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2))))),
    inference(congruence,[status(thm)],[c1269]) ).

cnf(c1271,plain,
    nand(nand(nand(X2,nand(X3,nand(X2,X4))),nand(X,nand(X3,nand(X2,X4)))),nand(nand(X2,nand(X3,nand(X2,X4))),nand(nand(X,nand(X3,nand(X2,X4))),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2))))) = nand(X2,nand(X3,nand(X2,X4))),
    inference(substitution,[status(thm)],[c514]) ).

cnf(c1272,plain,
    nand(nand(nand(X2,nand(X3,nand(X2,X4))),nand(X,nand(X3,nand(X2,X4)))),nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2))) = nand(X2,nand(X3,nand(X2,X4))),
    inference(transitivity,[status(thm)],[c1270,c1271]) ).

cnf(c1273,plain,
    nand(nand(nand(nand(nand(X4,X3),X3),X2),nand(nand(nand(X4,X3),X3),X2)),nand(nand(X2,nand(X3,nand(X2,X4))),nand(X,nand(X3,nand(X2,X4))))) = nand(X2,nand(X3,nand(X2,X4))),
    inference(transitivity,[status(thm)],[c1196,c1272]) ).

cnf(c1274,plain,
    nand(nand(nand(nand(nand(X,X3),X3),X2),nand(nand(nand(X,X3),X3),X2)),nand(nand(X2,nand(X3,nand(X2,X))),nand(nand(X3,nand(X2,X)),nand(X3,nand(X2,X))))) = nand(X2,nand(X3,nand(X2,X))),
    inference(substitution,[status(thm)],[c1273]) ).

cnf(c1275,plain,
    nand(nand(nand(nand(nand(X,X3),X3),X2),nand(nand(nand(X,X3),X3),X2)),nand(nand(X2,nand(X3,nand(X2,X))),nand(nand(X3,nand(X2,X)),nand(X2,X)))) = nand(X2,nand(X3,nand(X2,X))),
    inference(transitivity,[status(thm)],[c1195,c1274]) ).

cnf(c1276,plain,
    nand(nand(nand(nand(nand(X,X3),X3),X2),nand(nand(nand(X,X3),X3),X2)),nand(X3,nand(X2,X))) = nand(X2,nand(X3,nand(X2,X))),
    inference(transitivity,[status(thm)],[c1037,c1275]) ).

cnf(c1277,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(nand(nand(X,X3),X3),X2),nand(nand(nand(X,X3),X3),X2))) = nand(X2,nand(X3,nand(X2,X))),
    inference(transitivity,[status(thm)],[c1034,c1276]) ).

cnf(c1278,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(nand(nand(X,X3),X3),X2),nand(nand(X,X3),X3))) = nand(X2,nand(X3,nand(X2,X))),
    inference(transitivity,[status(thm)],[c1033,c1277]) ).

cnf(c1279,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(nand(nand(X,X3),X3),X2),nand(X3,nand(X2,X)))) = nand(X2,nand(X3,nand(X2,X))),
    inference(transitivity,[status(thm)],[c1032,c1278]) ).

cnf(c1280,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(X3,nand(X2,X)),nand(nand(nand(X,X3),X3),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3))))) = nand(X2,nand(X3,nand(X2,X))),
    inference(transitivity,[status(thm)],[c949,c1279]) ).

cnf(c1281,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(nand(nand(X,X3),X3),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3))),nand(nand(nand(X,X3),X3),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3))))) = nand(X2,nand(X3,nand(X2,X))),
    inference(transitivity,[status(thm)],[c844,c1280]) ).

cnf(c1282,plain,
    nand(nand(X3,nand(X2,X)),nand(nand(nand(nand(X,X3),X3),X2),nand(X,X3))) = nand(X2,nand(X3,nand(X2,X))),
    inference(transitivity,[status(thm)],[c843,c1281]) ).

cnf(c1283,plain,
    nand(nand(X2,nand(X3,X)),nand(nand(nand(nand(X,X2),X2),X3),nand(X,X2))) = nand(X3,nand(X2,nand(X3,X))),
    inference(substitution,[status(thm)],[c1282]) ).

cnf(c1284,plain,
    nand(nand(X,X2),nand(nand(X2,nand(X3,X)),nand(nand(nand(nand(X,X2),X2),X3),nand(X,X2)))) = nand(nand(X,X2),nand(X3,nand(X2,nand(X3,X)))),
    inference(congruence,[status(thm)],[c1283]) ).

cnf(c1285,plain,
    nand(nand(X3,nand(X2,nand(X3,X))),nand(X,X2)) = nand(nand(X,X2),nand(X3,nand(X2,nand(X3,X)))),
    inference(substitution,[status(thm)],[c248]) ).

cnf(c1286,plain,
    nand(nand(X,X2),nand(X3,nand(X2,nand(X3,X)))) = nand(nand(X3,nand(X2,nand(X3,X))),nand(X,X2)),
    inference(symmetry,[status(thm)],[c1285]) ).

cnf(c1287,plain,
    nand(nand(X,X2),nand(nand(X2,nand(X3,X)),nand(nand(nand(nand(X,X2),X2),X3),nand(X,X2)))) = nand(nand(X3,nand(X2,nand(X3,X))),nand(X,X2)),
    inference(transitivity,[status(thm)],[c1284,c1286]) ).

cnf(c1288,plain,
    nand(nand(X2,nand(nand(X,X2),X2)),nand(nand(X2,nand(X3,X)),nand(nand(nand(nand(X,X2),X2),X3),nand(X,X2)))) = nand(nand(X3,nand(X2,nand(X3,X))),nand(X,X2)),
    inference(transitivity,[status(thm)],[c824,c1287]) ).

cnf(c1289,plain,
    nand(nand(X2,nand(nand(X,X2),X2)),nand(nand(X2,nand(X3,X)),nand(nand(nand(nand(X,X2),X2),X3),nand(X2,nand(nand(X,X2),X2))))) = nand(nand(X3,nand(X2,nand(X3,X))),nand(X,X2)),
    inference(transitivity,[status(thm)],[c823,c1288]) ).

cnf(c1290,plain,
    nand(nand(X3,nand(nand(X2,X3),X3)),nand(nand(X3,nand(nand(X3,nand(X4,X2)),nand(X,nand(nand(nand(X2,X3),X3),nand(X3,nand(X4,X2)))))),nand(nand(nand(nand(X2,X3),X3),X4),nand(X3,nand(nand(X2,X3),X3))))) = nand(nand(X4,nand(X3,nand(X4,X2))),nand(X2,X3)),
    inference(transitivity,[status(thm)],[c820,c1289]) ).

cnf(c1291,plain,
    nand(nand(nand(nand(X,X2),X2),X3),nand(X2,nand(nand(X,X2),X2))) = nand(nand(X3,nand(X2,nand(X3,X))),nand(X,X2)),
    inference(transitivity,[status(thm)],[c740,c1290]) ).

cnf(c1292,plain,
    nand(nand(nand(nand(X,X2),X2),X3),nand(X,X2)) = nand(nand(X3,nand(X2,nand(X3,X))),nand(X,X2)),
    inference(transitivity,[status(thm)],[c724,c1291]) ).

cnf(c1293,plain,
    nand(nand(nand(nand(nand(X,X2),X2),X3),nand(X,X2)),nand(nand(X3,nand(X2,nand(X3,X))),X)) = nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X,X2)),nand(nand(X3,nand(X2,nand(X3,X))),X)),
    inference(congruence,[status(thm)],[c1292]) ).

cnf(c1294,plain,
    nand(nand(nand(X3,nand(X2,nand(X3,X))),nand(X,X2)),nand(nand(X3,nand(X2,nand(X3,X))),X)) = nand(X3,nand(X2,nand(X3,X))),
    inference(substitution,[status(thm)],[c260]) ).

cnf(c1295,plain,
    nand(nand(nand(nand(nand(X,X2),X2),X3),nand(X,X2)),nand(nand(X3,nand(X2,nand(X3,X))),X)) = nand(X3,nand(X2,nand(X3,X))),
    inference(transitivity,[status(thm)],[c1293,c1294]) ).

cnf(c1296,plain,
    nand(nand(nand(nand(nand(X,X2),X2),X3),nand(X,X2)),nand(nand(nand(nand(X,X2),X2),X3),X)) = nand(X3,nand(X2,nand(X3,X))),
    inference(transitivity,[status(thm)],[c722,c1295]) ).

cnf(c1297,plain,
    nand(nand(nand(X,X2),X2),X3) = nand(X3,nand(X2,nand(X3,X))),
    inference(transitivity,[status(thm)],[c262,c1296]) ).

cnf(c1298,plain,
    nand(nand(nand(c,b),b),a) = nand(a,nand(b,nand(a,c))),
    inference(substitution,[status(thm)],[c1297]) ).

cnf(c1299,plain,
    nand(a,nand(b,nand(a,c))) = nand(nand(nand(c,b),b),a),
    inference(symmetry,[status(thm)],[c1298]) ).

cnf(c1300,plain,
    $false,
    inference(resolution,[status(thm)],[c1,c1299]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : BOO076-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.21  % Computer : n011.cluster.edu
% 0.06/0.21  % Model    : x86_64 x86_64
% 0.06/0.21  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.21  % Memory   : 8046.5625MB
% 0.06/0.21  % OS       : Linux 6.8.0-71-generic
% 0.06/0.21  % CPULimit : 300
% 0.06/0.21  % WCLimit  : 300
% 0.06/0.21  % DateTime : Mon Sep 28 21:08:15 UTC 2026
% 0.06/0.21  % CPUTime  : 
% 0.06/0.21  Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 76.27/9.97  Command-line arguments: --flatten --complete-subsets
% 76.27/9.97  
% 76.27/9.97  % SZS status Unsatisfiable
% 76.27/9.97  
% 80.01/10.39  % SZS output start CNFRefutation
% See solution above
% 93.72/12.22  
% 93.72/12.22  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------