Twee---2.7.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL400-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n009.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 11:49:46 AM UTC 2026

% Result   : Unsatisfiable 81.82s 10.90s
% Output   : CNFRefutation 86.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   87
%            Number of leaves      :    6
% Syntax   : Number of clauses     :  529 ( 529 unt;   0 nHn;   3 RR)
%            Number of literals    :  529 ( 528 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   11 (   3 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-4 aty)
%            Number of variables   : 1567 ( 223 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
    is_a_theorem(implies(not(implies(x,y)),x)) != true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_66) ).

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

cnf(c3,plain,
    ifeq(true,true,is_a_theorem(implies(not(implies(X3,X2)),X3)),true) = is_a_theorem(implies(not(implies(X3,X2)),X3)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c4,plain,
    is_a_theorem(implies(not(implies(X3,X2)),X3)) = ifeq(true,true,is_a_theorem(implies(not(implies(X3,X2)),X3)),true),
    inference(symmetry,[status(thm)],[c3]) ).

cnf(c5,plain,
    ifeq(true,true,is_a_theorem(implies(not(implies(X3,X2)),implies(X2,X4))),true) = is_a_theorem(implies(not(implies(X3,X2)),implies(X2,X4))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c6,plain,
    is_a_theorem(implies(not(implies(X4,X3)),implies(X3,X2))) = ifeq(true,true,is_a_theorem(implies(not(implies(X4,X3)),implies(X3,X2))),true),
    inference(symmetry,[status(thm)],[c5]) ).

cnf(c7,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(not(X3),implies(X4,X2)))),true) = is_a_theorem(implies(implies(X4,X3),implies(not(X3),implies(X4,X2)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c8,plain,
    is_a_theorem(implies(implies(X4,X3),implies(not(X3),implies(X4,X2)))) = ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(not(X3),implies(X4,X2)))),true),
    inference(symmetry,[status(thm)],[c7]) ).

cnf(c9,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X4,X3),X2),implies(not(X4),X2))),true) = is_a_theorem(implies(implies(implies(X4,X3),X2),implies(not(X4),X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c10,plain,
    is_a_theorem(implies(implies(implies(X4,X3),X2),implies(not(X4),X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(X4,X3),X2),implies(not(X4),X2))),true),
    inference(symmetry,[status(thm)],[c9]) ).

cnf(c11,plain,
    ifeq(true,true,is_a_theorem(implies(implies(not(not(X3)),not(X3)),implies(X3,X2))),true) = is_a_theorem(implies(implies(not(not(X3)),not(X3)),implies(X3,X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c12,plain,
    is_a_theorem(implies(implies(not(not(X3)),not(X3)),implies(X3,X2))) = ifeq(true,true,is_a_theorem(implies(implies(not(not(X3)),not(X3)),implies(X3,X2))),true),
    inference(symmetry,[status(thm)],[c11]) ).

cnf(c13,plain,
    ifeq(true,true,is_a_theorem(implies(X2,not(implies(not(not(X2)),not(X2))))),true) = is_a_theorem(implies(X2,not(implies(not(not(X2)),not(X2))))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c14,plain,
    is_a_theorem(implies(X2,not(implies(not(not(X2)),not(X2))))) = ifeq(true,true,is_a_theorem(implies(X2,not(implies(not(not(X2)),not(X2))))),true),
    inference(symmetry,[status(thm)],[c13]) ).

cnf(c15,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X3,X2),not(implies(X3,X2))),not(implies(X3,X2)))),true) = is_a_theorem(implies(implies(implies(X3,X2),not(implies(X3,X2))),not(implies(X3,X2)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c16,plain,
    is_a_theorem(implies(implies(implies(X3,X2),not(implies(X3,X2))),not(implies(X3,X2)))) = ifeq(true,true,is_a_theorem(implies(implies(implies(X3,X2),not(implies(X3,X2))),not(implies(X3,X2)))),true),
    inference(symmetry,[status(thm)],[c15]) ).

cnf(c17,plain,
    ifeq(true,true,is_a_theorem(implies(implies(not(implies(X4,X3)),X2),implies(implies(implies(X4,X3),not(implies(X4,X3))),X2))),true) = is_a_theorem(implies(implies(not(implies(X4,X3)),X2),implies(implies(implies(X4,X3),not(implies(X4,X3))),X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c18,plain,
    is_a_theorem(implies(implies(not(implies(X4,X3)),X2),implies(implies(implies(X4,X3),not(implies(X4,X3))),X2))) = ifeq(true,true,is_a_theorem(implies(implies(not(implies(X4,X3)),X2),implies(implies(implies(X4,X3),not(implies(X4,X3))),X2))),true),
    inference(symmetry,[status(thm)],[c17]) ).

cnf(c19,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X4,X3),X2),implies(not(not(implies(X4,X3))),X2))),true) = is_a_theorem(implies(implies(implies(X4,X3),X2),implies(not(not(implies(X4,X3))),X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c20,plain,
    is_a_theorem(implies(implies(implies(X4,X3),X2),implies(not(not(implies(X4,X3))),X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(X4,X3),X2),implies(not(not(implies(X4,X3))),X2))),true),
    inference(symmetry,[status(thm)],[c19]) ).

cnf(c21,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X4,implies(X3,X2)),X5),implies(not(X4),X5))),true) = is_a_theorem(implies(implies(implies(X4,implies(X3,X2)),X5),implies(not(X4),X5))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c22,plain,
    is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(not(X5),X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(not(X5),X2))),true),
    inference(symmetry,[status(thm)],[c21]) ).

cnf(c23,plain,
    ifeq(true,true,is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))),true) = is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c24,plain,
    is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))) = ifeq(true,true,is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))),true),
    inference(symmetry,[status(thm)],[c23]) ).

cnf(c25,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(not(X3)),not(X3))),implies(X3,implies(X4,X2)))),true) = is_a_theorem(implies(implies(X4,implies(not(not(X3)),not(X3))),implies(X3,implies(X4,X2)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c26,plain,
    is_a_theorem(implies(implies(X4,implies(not(not(X3)),not(X3))),implies(X3,implies(X4,X2)))) = ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(not(X3)),not(X3))),implies(X3,implies(X4,X2)))),true),
    inference(symmetry,[status(thm)],[c25]) ).

cnf(c27,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))),true) = is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c28,plain,
    is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))),true),
    inference(symmetry,[status(thm)],[c27]) ).

cnf(c29,plain,
    ifeq(true,true,is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))),true) = is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c30,plain,
    is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))) = ifeq(true,true,is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))),true),
    inference(symmetry,[status(thm)],[c29]) ).

cnf(c31,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),true) = is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c32,plain,
    is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))) = ifeq(true,true,is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),true),
    inference(symmetry,[status(thm)],[c31]) ).

cnf(c33,axiom,
    is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_1) ).

cnf(c34,plain,
    is_a_theorem(implies(implies(implies(not(X3),X3),X3),implies(implies(X3,X2),implies(implies(not(X3),X3),X2)))) = true,
    inference(substitution,[status(thm)],[c33]) ).

cnf(c35,plain,
    true = is_a_theorem(implies(implies(implies(not(X3),X3),X3),implies(implies(X3,X2),implies(implies(not(X3),X3),X2)))),
    inference(symmetry,[status(thm)],[c34]) ).

cnf(c36,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),true) = ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),implies(implies(X3,X2),implies(implies(not(X3),X3),X2)))),true,is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),true),
    inference(congruence,[status(thm)],[c35]) ).

cnf(c37,plain,
    ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c38,plain,
    is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
    inference(symmetry,[status(thm)],[c37]) ).

cnf(c39,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
    inference(congruence,[status(thm)],[c38]) ).

cnf(c40,axiom,
    is_a_theorem(implies(implies(not(X2),X2),X2)) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).

cnf(c41,plain,
    true = is_a_theorem(implies(implies(not(X2),X2),X2)),
    inference(symmetry,[status(thm)],[c40]) ).

cnf(c42,plain,
    ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(not(X3),X3),X3)),true,is_a_theorem(X2),true),
    inference(congruence,[status(thm)],[c41]) ).

cnf(c43,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,ifeq(is_a_theorem(implies(implies(not(X3),X3),X3)),true,is_a_theorem(X2),true),true),
    inference(congruence,[status(thm)],[c42]) ).

cnf(c44,axiom,
    ifeq(is_a_theorem(implies(X2,Y2)),true,ifeq(is_a_theorem(X2),true,is_a_theorem(Y2),true),true) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).

cnf(c45,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,ifeq(is_a_theorem(implies(implies(not(X3),X3),X3)),true,is_a_theorem(X2),true),true) = true,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c46,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
    inference(transitivity,[status(thm)],[c43,c45]) ).

cnf(c47,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),X2)),true,is_a_theorem(X2),true) = true,
    inference(transitivity,[status(thm)],[c39,c46]) ).

cnf(c48,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(X3),X3),X3),implies(implies(X3,X2),implies(implies(not(X3),X3),X2)))),true,is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),true) = true,
    inference(substitution,[status(thm)],[c47]) ).

cnf(c49,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),true) = true,
    inference(transitivity,[status(thm)],[c36,c48]) ).

cnf(c50,plain,
    is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))) = true,
    inference(transitivity,[status(thm)],[c32,c49]) ).

cnf(c51,plain,
    is_a_theorem(implies(implies(not(X3),X2),implies(implies(not(not(X3)),not(X3)),X2))) = true,
    inference(substitution,[status(thm)],[c50]) ).

cnf(c52,plain,
    true = is_a_theorem(implies(implies(not(X3),X2),implies(implies(not(not(X3)),not(X3)),X2))),
    inference(symmetry,[status(thm)],[c51]) ).

cnf(c53,plain,
    ifeq(true,true,is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))),true) = ifeq(is_a_theorem(implies(implies(not(X3),X2),implies(implies(not(not(X3)),not(X3)),X2))),true,is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))),true),
    inference(congruence,[status(thm)],[c52]) ).

cnf(c54,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c55,plain,
    ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true) = ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true),
    inference(symmetry,[status(thm)],[c54]) ).

cnf(c56,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true) = is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c57,plain,
    is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true),
    inference(symmetry,[status(thm)],[c56]) ).

cnf(c58,plain,
    is_a_theorem(implies(implies(X4,implies(not(X4),X3)),implies(implies(implies(not(X4),X3),X2),implies(X4,X2)))) = true,
    inference(substitution,[status(thm)],[c33]) ).

cnf(c59,plain,
    true = is_a_theorem(implies(implies(X4,implies(not(X4),X3)),implies(implies(implies(not(X4),X3),X2),implies(X4,X2)))),
    inference(symmetry,[status(thm)],[c58]) ).

cnf(c60,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true) = ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),implies(implies(implies(not(X4),X3),X2),implies(X4,X2)))),true,is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true),
    inference(congruence,[status(thm)],[c59]) ).

cnf(c61,plain,
    ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c62,plain,
    is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
    inference(symmetry,[status(thm)],[c61]) ).

cnf(c63,plain,
    ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
    inference(congruence,[status(thm)],[c62]) ).

cnf(c64,axiom,
    is_a_theorem(implies(X2,implies(not(X2),Y2))) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_3) ).

cnf(c65,plain,
    is_a_theorem(implies(X3,implies(not(X3),X2))) = true,
    inference(substitution,[status(thm)],[c64]) ).

cnf(c66,plain,
    true = is_a_theorem(implies(X3,implies(not(X3),X2))),
    inference(symmetry,[status(thm)],[c65]) ).

cnf(c67,plain,
    ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(X4,implies(not(X4),X3))),true,is_a_theorem(X2),true),
    inference(congruence,[status(thm)],[c66]) ).

cnf(c68,plain,
    ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,ifeq(is_a_theorem(implies(X4,implies(not(X4),X3))),true,is_a_theorem(X2),true),true),
    inference(congruence,[status(thm)],[c67]) ).

cnf(c69,plain,
    ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,ifeq(is_a_theorem(implies(X4,implies(not(X4),X3))),true,is_a_theorem(X2),true),true) = true,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c70,plain,
    ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
    inference(transitivity,[status(thm)],[c68,c69]) ).

cnf(c71,plain,
    ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),X2)),true,is_a_theorem(X2),true) = true,
    inference(transitivity,[status(thm)],[c63,c70]) ).

cnf(c72,plain,
    ifeq(is_a_theorem(implies(implies(X4,implies(not(X4),X3)),implies(implies(implies(not(X4),X3),X2),implies(X4,X2)))),true,is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true) = true,
    inference(substitution,[status(thm)],[c71]) ).

cnf(c73,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true) = true,
    inference(transitivity,[status(thm)],[c60,c72]) ).

cnf(c74,plain,
    is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))) = true,
    inference(transitivity,[status(thm)],[c57,c73]) ).

cnf(c75,plain,
    true = is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),
    inference(symmetry,[status(thm)],[c74]) ).

cnf(c76,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true,ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true),
    inference(congruence,[status(thm)],[c75]) ).

cnf(c77,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),true,ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = true,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c78,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = true,
    inference(transitivity,[status(thm)],[c76,c77]) ).

cnf(c79,plain,
    ifeq(is_a_theorem(implies(implies(not(X4),X3),X2)),true,is_a_theorem(implies(X4,X2)),true) = true,
    inference(transitivity,[status(thm)],[c55,c78]) ).

cnf(c80,plain,
    ifeq(is_a_theorem(implies(implies(not(X3),X2),implies(implies(not(not(X3)),not(X3)),X2))),true,is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))),true) = true,
    inference(substitution,[status(thm)],[c79]) ).

cnf(c81,plain,
    ifeq(true,true,is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))),true) = true,
    inference(transitivity,[status(thm)],[c53,c80]) ).

cnf(c82,plain,
    is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))) = true,
    inference(transitivity,[status(thm)],[c30,c81]) ).

cnf(c83,plain,
    true = is_a_theorem(implies(X3,implies(implies(not(not(X3)),not(X3)),X2))),
    inference(symmetry,[status(thm)],[c82]) ).

cnf(c84,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))),true) = ifeq(is_a_theorem(implies(X4,implies(implies(not(not(X4)),not(X4)),X3))),true,is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))),true),
    inference(congruence,[status(thm)],[c83]) ).

cnf(c85,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c86,plain,
    ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true) = ifeq(true,true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true),
    inference(symmetry,[status(thm)],[c85]) ).

cnf(c87,plain,
    is_a_theorem(implies(implies(X4,X3),implies(implies(X3,X2),implies(X4,X2)))) = true,
    inference(substitution,[status(thm)],[c33]) ).

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

cnf(c89,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = ifeq(is_a_theorem(implies(implies(X4,X3),implies(implies(X3,X2),implies(X4,X2)))),true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true),
    inference(congruence,[status(thm)],[c88]) ).

cnf(c90,plain,
    ifeq(is_a_theorem(implies(implies(X4,X3),implies(implies(X3,X2),implies(X4,X2)))),true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = true,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c91,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = true,
    inference(transitivity,[status(thm)],[c89,c90]) ).

cnf(c92,plain,
    ifeq(is_a_theorem(implies(X4,X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true) = true,
    inference(transitivity,[status(thm)],[c86,c91]) ).

cnf(c93,plain,
    ifeq(is_a_theorem(implies(X4,implies(implies(not(not(X4)),not(X4)),X3))),true,is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))),true) = true,
    inference(substitution,[status(thm)],[c92]) ).

cnf(c94,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))),true) = true,
    inference(transitivity,[status(thm)],[c84,c93]) ).

cnf(c95,plain,
    is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))) = true,
    inference(transitivity,[status(thm)],[c28,c94]) ).

cnf(c96,plain,
    is_a_theorem(implies(implies(implies(implies(not(not(X3)),not(X3)),X2),implies(X4,X2)),implies(X3,implies(X4,X2)))) = true,
    inference(substitution,[status(thm)],[c95]) ).

cnf(c97,plain,
    true = is_a_theorem(implies(implies(implies(implies(not(not(X3)),not(X3)),X2),implies(X4,X2)),implies(X3,implies(X4,X2)))),
    inference(symmetry,[status(thm)],[c96]) ).

cnf(c98,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(not(X3)),not(X3))),implies(X3,implies(X4,X2)))),true) = ifeq(is_a_theorem(implies(implies(implies(implies(not(not(X3)),not(X3)),X2),implies(X4,X2)),implies(X3,implies(X4,X2)))),true,is_a_theorem(implies(implies(X4,implies(not(not(X3)),not(X3))),implies(X3,implies(X4,X2)))),true),
    inference(congruence,[status(thm)],[c97]) ).

cnf(c99,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c100,plain,
    ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true) = ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),true),
    inference(symmetry,[status(thm)],[c99]) ).

cnf(c101,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true) = is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c102,plain,
    is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true),
    inference(symmetry,[status(thm)],[c101]) ).

cnf(c103,plain,
    is_a_theorem(implies(implies(X2,X4),implies(implies(X4,X3),implies(X2,X3)))) = true,
    inference(substitution,[status(thm)],[c33]) ).

cnf(c104,plain,
    true = is_a_theorem(implies(implies(X2,X4),implies(implies(X4,X3),implies(X2,X3)))),
    inference(symmetry,[status(thm)],[c103]) ).

cnf(c105,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true) = ifeq(is_a_theorem(implies(implies(X3,X5),implies(implies(X5,X4),implies(X3,X4)))),true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true),
    inference(congruence,[status(thm)],[c104]) ).

cnf(c106,plain,
    ifeq(is_a_theorem(implies(implies(X3,X5),implies(implies(X5,X4),implies(X3,X4)))),true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true) = true,
    inference(substitution,[status(thm)],[c92]) ).

cnf(c107,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true) = true,
    inference(transitivity,[status(thm)],[c105,c106]) ).

cnf(c108,plain,
    is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))) = true,
    inference(transitivity,[status(thm)],[c102,c107]) ).

cnf(c109,plain,
    true = is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),
    inference(symmetry,[status(thm)],[c108]) ).

cnf(c110,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true,ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),true),
    inference(congruence,[status(thm)],[c109]) ).

cnf(c111,plain,
    ifeq(is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(implies(X3,X5),X2))),true,ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),true) = true,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c112,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true),true) = true,
    inference(transitivity,[status(thm)],[c110,c111]) ).

cnf(c113,plain,
    ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(X3,X4)),X2)),true,is_a_theorem(implies(implies(X3,X5),X2)),true) = true,
    inference(transitivity,[status(thm)],[c100,c112]) ).

cnf(c114,plain,
    ifeq(is_a_theorem(implies(implies(implies(implies(not(not(X3)),not(X3)),X2),implies(X4,X2)),implies(X3,implies(X4,X2)))),true,is_a_theorem(implies(implies(X4,implies(not(not(X3)),not(X3))),implies(X3,implies(X4,X2)))),true) = true,
    inference(substitution,[status(thm)],[c113]) ).

cnf(c115,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(not(X3)),not(X3))),implies(X3,implies(X4,X2)))),true) = true,
    inference(transitivity,[status(thm)],[c98,c114]) ).

cnf(c116,plain,
    is_a_theorem(implies(implies(X4,implies(not(not(X3)),not(X3))),implies(X3,implies(X4,X2)))) = true,
    inference(transitivity,[status(thm)],[c26,c115]) ).

cnf(c117,plain,
    is_a_theorem(implies(implies(X3,implies(not(not(X4)),not(X4))),implies(X4,implies(X3,X2)))) = true,
    inference(substitution,[status(thm)],[c116]) ).

cnf(c118,plain,
    true = is_a_theorem(implies(implies(X3,implies(not(not(X4)),not(X4))),implies(X4,implies(X3,X2)))),
    inference(symmetry,[status(thm)],[c117]) ).

cnf(c119,plain,
    ifeq(true,true,is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))),true) = ifeq(is_a_theorem(implies(implies(X3,implies(not(not(X4)),not(X4))),implies(X4,implies(X3,X2)))),true,is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))),true),
    inference(congruence,[status(thm)],[c118]) ).

cnf(c120,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(implies(X5,implies(not(X4),X3)),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = ifeq(is_a_theorem(implies(implies(X5,implies(not(X4),X3)),X2)),true,is_a_theorem(implies(X4,X2)),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c121,plain,
    ifeq(is_a_theorem(implies(implies(X5,implies(not(X4),X3)),X2)),true,is_a_theorem(implies(X4,X2)),true) = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X5,implies(not(X4),X3)),X2)),true,is_a_theorem(implies(X4,X2)),true),true),
    inference(symmetry,[status(thm)],[c120]) ).

cnf(c122,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),true) = is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c123,plain,
    is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),true),
    inference(symmetry,[status(thm)],[c122]) ).

cnf(c124,plain,
    ifeq(true,true,is_a_theorem(implies(X4,implies(X3,implies(not(X4),X2)))),true) = is_a_theorem(implies(X4,implies(X3,implies(not(X4),X2)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c125,plain,
    is_a_theorem(implies(X4,implies(X3,implies(not(X4),X2)))) = ifeq(true,true,is_a_theorem(implies(X4,implies(X3,implies(not(X4),X2)))),true),
    inference(symmetry,[status(thm)],[c124]) ).

cnf(c126,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(not(X3),X4)),X2),implies(X3,X2))),true) = is_a_theorem(implies(implies(implies(implies(X5,X4),implies(not(X3),X4)),X2),implies(X3,X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c127,plain,
    is_a_theorem(implies(implies(implies(implies(X5,X4),implies(not(X3),X4)),X2),implies(X3,X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(not(X3),X4)),X2),implies(X3,X2))),true),
    inference(symmetry,[status(thm)],[c126]) ).

cnf(c128,plain,
    ifeq(true,true,is_a_theorem(implies(X4,implies(implies(X3,X2),implies(not(X4),X2)))),true) = is_a_theorem(implies(X4,implies(implies(X3,X2),implies(not(X4),X2)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c129,plain,
    is_a_theorem(implies(X4,implies(implies(X3,X2),implies(not(X4),X2)))) = ifeq(true,true,is_a_theorem(implies(X4,implies(implies(X3,X2),implies(not(X4),X2)))),true),
    inference(symmetry,[status(thm)],[c128]) ).

cnf(c130,plain,
    is_a_theorem(implies(implies(not(X4),X3),implies(implies(X3,X2),implies(not(X4),X2)))) = true,
    inference(substitution,[status(thm)],[c33]) ).

cnf(c131,plain,
    true = is_a_theorem(implies(implies(not(X4),X3),implies(implies(X3,X2),implies(not(X4),X2)))),
    inference(symmetry,[status(thm)],[c130]) ).

cnf(c132,plain,
    ifeq(true,true,is_a_theorem(implies(X4,implies(implies(X3,X2),implies(not(X4),X2)))),true) = ifeq(is_a_theorem(implies(implies(not(X4),X3),implies(implies(X3,X2),implies(not(X4),X2)))),true,is_a_theorem(implies(X4,implies(implies(X3,X2),implies(not(X4),X2)))),true),
    inference(congruence,[status(thm)],[c131]) ).

cnf(c133,plain,
    ifeq(is_a_theorem(implies(implies(not(X4),X3),implies(implies(X3,X2),implies(not(X4),X2)))),true,is_a_theorem(implies(X4,implies(implies(X3,X2),implies(not(X4),X2)))),true) = true,
    inference(substitution,[status(thm)],[c79]) ).

cnf(c134,plain,
    ifeq(true,true,is_a_theorem(implies(X4,implies(implies(X3,X2),implies(not(X4),X2)))),true) = true,
    inference(transitivity,[status(thm)],[c132,c133]) ).

cnf(c135,plain,
    is_a_theorem(implies(X4,implies(implies(X3,X2),implies(not(X4),X2)))) = true,
    inference(transitivity,[status(thm)],[c129,c134]) ).

cnf(c136,plain,
    is_a_theorem(implies(X2,implies(implies(X4,X3),implies(not(X2),X3)))) = true,
    inference(substitution,[status(thm)],[c135]) ).

cnf(c137,plain,
    true = is_a_theorem(implies(X2,implies(implies(X4,X3),implies(not(X2),X3)))),
    inference(symmetry,[status(thm)],[c136]) ).

cnf(c138,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(not(X3),X4)),X2),implies(X3,X2))),true) = ifeq(is_a_theorem(implies(X3,implies(implies(X5,X4),implies(not(X3),X4)))),true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(not(X3),X4)),X2),implies(X3,X2))),true),
    inference(congruence,[status(thm)],[c137]) ).

cnf(c139,plain,
    ifeq(is_a_theorem(implies(X3,implies(implies(X5,X4),implies(not(X3),X4)))),true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(not(X3),X4)),X2),implies(X3,X2))),true) = true,
    inference(substitution,[status(thm)],[c92]) ).

cnf(c140,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(not(X3),X4)),X2),implies(X3,X2))),true) = true,
    inference(transitivity,[status(thm)],[c138,c139]) ).

cnf(c141,plain,
    is_a_theorem(implies(implies(implies(implies(X5,X4),implies(not(X3),X4)),X2),implies(X3,X2))) = true,
    inference(transitivity,[status(thm)],[c127,c140]) ).

cnf(c142,plain,
    is_a_theorem(implies(implies(implies(implies(not(X3),X2),implies(not(X4),X2)),implies(X3,implies(not(X4),X2))),implies(X4,implies(X3,implies(not(X4),X2))))) = true,
    inference(substitution,[status(thm)],[c141]) ).

cnf(c143,plain,
    true = is_a_theorem(implies(implies(implies(implies(not(X3),X2),implies(not(X4),X2)),implies(X3,implies(not(X4),X2))),implies(X4,implies(X3,implies(not(X4),X2))))),
    inference(symmetry,[status(thm)],[c142]) ).

cnf(c144,plain,
    ifeq(true,true,is_a_theorem(implies(X4,implies(X3,implies(not(X4),X2)))),true) = ifeq(is_a_theorem(implies(implies(implies(implies(not(X3),X2),implies(not(X4),X2)),implies(X3,implies(not(X4),X2))),implies(X4,implies(X3,implies(not(X4),X2))))),true,is_a_theorem(implies(X4,implies(X3,implies(not(X4),X2)))),true),
    inference(congruence,[status(thm)],[c143]) ).

cnf(c145,plain,
    ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c146,plain,
    is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
    inference(symmetry,[status(thm)],[c145]) ).

cnf(c147,plain,
    ifeq(is_a_theorem(implies(implies(implies(implies(not(X5),X4),X3),implies(X5,X3)),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(implies(implies(not(X5),X4),X3),implies(X5,X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
    inference(congruence,[status(thm)],[c146]) ).

cnf(c148,plain,
    true = is_a_theorem(implies(implies(implies(not(X4),X3),X2),implies(X4,X2))),
    inference(symmetry,[status(thm)],[c74]) ).

cnf(c149,plain,
    ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(implies(not(X5),X4),X3),implies(X5,X3))),true,is_a_theorem(X2),true),
    inference(congruence,[status(thm)],[c148]) ).

cnf(c150,plain,
    ifeq(is_a_theorem(implies(implies(implies(implies(not(X5),X4),X3),implies(X5,X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(implies(implies(implies(implies(not(X5),X4),X3),implies(X5,X3)),X2)),true,ifeq(is_a_theorem(implies(implies(implies(not(X5),X4),X3),implies(X5,X3))),true,is_a_theorem(X2),true),true),
    inference(congruence,[status(thm)],[c149]) ).

cnf(c151,plain,
    ifeq(is_a_theorem(implies(implies(implies(implies(not(X5),X4),X3),implies(X5,X3)),X2)),true,ifeq(is_a_theorem(implies(implies(implies(not(X5),X4),X3),implies(X5,X3))),true,is_a_theorem(X2),true),true) = true,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c152,plain,
    ifeq(is_a_theorem(implies(implies(implies(implies(not(X5),X4),X3),implies(X5,X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
    inference(transitivity,[status(thm)],[c150,c151]) ).

cnf(c153,plain,
    ifeq(is_a_theorem(implies(implies(implies(implies(not(X5),X4),X3),implies(X5,X3)),X2)),true,is_a_theorem(X2),true) = true,
    inference(transitivity,[status(thm)],[c147,c152]) ).

cnf(c154,plain,
    ifeq(is_a_theorem(implies(implies(implies(implies(not(X3),X2),implies(not(X4),X2)),implies(X3,implies(not(X4),X2))),implies(X4,implies(X3,implies(not(X4),X2))))),true,is_a_theorem(implies(X4,implies(X3,implies(not(X4),X2)))),true) = true,
    inference(substitution,[status(thm)],[c153]) ).

cnf(c155,plain,
    ifeq(true,true,is_a_theorem(implies(X4,implies(X3,implies(not(X4),X2)))),true) = true,
    inference(transitivity,[status(thm)],[c144,c154]) ).

cnf(c156,plain,
    is_a_theorem(implies(X4,implies(X3,implies(not(X4),X2)))) = true,
    inference(transitivity,[status(thm)],[c125,c155]) ).

cnf(c157,plain,
    is_a_theorem(implies(X3,implies(X4,implies(not(X3),X2)))) = true,
    inference(substitution,[status(thm)],[c156]) ).

cnf(c158,plain,
    true = is_a_theorem(implies(X3,implies(X4,implies(not(X3),X2)))),
    inference(symmetry,[status(thm)],[c157]) ).

cnf(c159,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),true) = ifeq(is_a_theorem(implies(X4,implies(X5,implies(not(X4),X3)))),true,is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),true),
    inference(congruence,[status(thm)],[c158]) ).

cnf(c160,plain,
    ifeq(is_a_theorem(implies(X4,implies(X5,implies(not(X4),X3)))),true,is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),true) = true,
    inference(substitution,[status(thm)],[c92]) ).

cnf(c161,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),true) = true,
    inference(transitivity,[status(thm)],[c159,c160]) ).

cnf(c162,plain,
    is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))) = true,
    inference(transitivity,[status(thm)],[c123,c161]) ).

cnf(c163,plain,
    true = is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),
    inference(symmetry,[status(thm)],[c162]) ).

cnf(c164,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(implies(X5,implies(not(X4),X3)),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),true,ifeq(is_a_theorem(implies(implies(X5,implies(not(X4),X3)),X2)),true,is_a_theorem(implies(X4,X2)),true),true),
    inference(congruence,[status(thm)],[c163]) ).

cnf(c165,plain,
    ifeq(is_a_theorem(implies(implies(implies(X5,implies(not(X4),X3)),X2),implies(X4,X2))),true,ifeq(is_a_theorem(implies(implies(X5,implies(not(X4),X3)),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = true,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c166,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(implies(X5,implies(not(X4),X3)),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = true,
    inference(transitivity,[status(thm)],[c164,c165]) ).

cnf(c167,plain,
    ifeq(is_a_theorem(implies(implies(X5,implies(not(X4),X3)),X2)),true,is_a_theorem(implies(X4,X2)),true) = true,
    inference(transitivity,[status(thm)],[c121,c166]) ).

cnf(c168,plain,
    ifeq(is_a_theorem(implies(implies(X3,implies(not(not(X4)),not(X4))),implies(X4,implies(X3,X2)))),true,is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))),true) = true,
    inference(substitution,[status(thm)],[c167]) ).

cnf(c169,plain,
    ifeq(true,true,is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))),true) = true,
    inference(transitivity,[status(thm)],[c119,c168]) ).

cnf(c170,plain,
    is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))) = true,
    inference(transitivity,[status(thm)],[c24,c169]) ).

cnf(c171,plain,
    true = is_a_theorem(implies(not(X4),implies(X4,implies(X3,X2)))),
    inference(symmetry,[status(thm)],[c170]) ).

cnf(c172,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(not(X5),X2))),true) = ifeq(is_a_theorem(implies(not(X5),implies(X5,implies(X4,X3)))),true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(not(X5),X2))),true),
    inference(congruence,[status(thm)],[c171]) ).

cnf(c173,plain,
    ifeq(is_a_theorem(implies(not(X5),implies(X5,implies(X4,X3)))),true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(not(X5),X2))),true) = true,
    inference(substitution,[status(thm)],[c92]) ).

cnf(c174,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(not(X5),X2))),true) = true,
    inference(transitivity,[status(thm)],[c172,c173]) ).

cnf(c175,plain,
    is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(not(X5),X2))) = true,
    inference(transitivity,[status(thm)],[c22,c174]) ).

cnf(c176,plain,
    is_a_theorem(implies(implies(implies(not(implies(X4,X3)),implies(X4,X3)),X2),implies(not(not(implies(X4,X3))),X2))) = true,
    inference(substitution,[status(thm)],[c175]) ).

cnf(c177,plain,
    true = is_a_theorem(implies(implies(implies(not(implies(X4,X3)),implies(X4,X3)),X2),implies(not(not(implies(X4,X3))),X2))),
    inference(symmetry,[status(thm)],[c176]) ).

cnf(c178,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X4,X3),X2),implies(not(not(implies(X4,X3))),X2))),true) = ifeq(is_a_theorem(implies(implies(implies(not(implies(X4,X3)),implies(X4,X3)),X2),implies(not(not(implies(X4,X3))),X2))),true,is_a_theorem(implies(implies(implies(X4,X3),X2),implies(not(not(implies(X4,X3))),X2))),true),
    inference(congruence,[status(thm)],[c177]) ).

cnf(c179,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c180,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true) = ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),true),
    inference(symmetry,[status(thm)],[c179]) ).

cnf(c181,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true) = is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c182,plain,
    is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true),
    inference(symmetry,[status(thm)],[c181]) ).

cnf(c183,plain,
    true = is_a_theorem(implies(implies(X3,X2),implies(implies(not(X3),X3),X2))),
    inference(symmetry,[status(thm)],[c50]) ).

cnf(c184,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true) = ifeq(is_a_theorem(implies(implies(X4,X3),implies(implies(not(X4),X4),X3))),true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true),
    inference(congruence,[status(thm)],[c183]) ).

cnf(c185,plain,
    ifeq(is_a_theorem(implies(implies(X4,X3),implies(implies(not(X4),X4),X3))),true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true) = true,
    inference(substitution,[status(thm)],[c92]) ).

cnf(c186,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true) = true,
    inference(transitivity,[status(thm)],[c184,c185]) ).

cnf(c187,plain,
    is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))) = true,
    inference(transitivity,[status(thm)],[c182,c186]) ).

cnf(c188,plain,
    true = is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),
    inference(symmetry,[status(thm)],[c187]) ).

cnf(c189,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true,ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),true),
    inference(congruence,[status(thm)],[c188]) ).

cnf(c190,plain,
    ifeq(is_a_theorem(implies(implies(implies(implies(not(X4),X4),X3),X2),implies(implies(X4,X3),X2))),true,ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),true) = true,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c191,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true),true) = true,
    inference(transitivity,[status(thm)],[c189,c190]) ).

cnf(c192,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(X4),X4),X3),X2)),true,is_a_theorem(implies(implies(X4,X3),X2)),true) = true,
    inference(transitivity,[status(thm)],[c180,c191]) ).

cnf(c193,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(implies(X4,X3)),implies(X4,X3)),X2),implies(not(not(implies(X4,X3))),X2))),true,is_a_theorem(implies(implies(implies(X4,X3),X2),implies(not(not(implies(X4,X3))),X2))),true) = true,
    inference(substitution,[status(thm)],[c192]) ).

cnf(c194,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X4,X3),X2),implies(not(not(implies(X4,X3))),X2))),true) = true,
    inference(transitivity,[status(thm)],[c178,c193]) ).

cnf(c195,plain,
    is_a_theorem(implies(implies(implies(X4,X3),X2),implies(not(not(implies(X4,X3))),X2))) = true,
    inference(transitivity,[status(thm)],[c20,c194]) ).

cnf(c196,plain,
    is_a_theorem(implies(implies(implies(X3,X2),not(implies(X3,X2))),implies(not(not(implies(X3,X2))),not(implies(X3,X2))))) = true,
    inference(substitution,[status(thm)],[c195]) ).

cnf(c197,plain,
    true = is_a_theorem(implies(implies(implies(X3,X2),not(implies(X3,X2))),implies(not(not(implies(X3,X2))),not(implies(X3,X2))))),
    inference(symmetry,[status(thm)],[c196]) ).

cnf(c198,plain,
    ifeq(true,true,is_a_theorem(implies(implies(not(implies(X4,X3)),X2),implies(implies(implies(X4,X3),not(implies(X4,X3))),X2))),true) = ifeq(is_a_theorem(implies(implies(implies(X4,X3),not(implies(X4,X3))),implies(not(not(implies(X4,X3))),not(implies(X4,X3))))),true,is_a_theorem(implies(implies(not(implies(X4,X3)),X2),implies(implies(implies(X4,X3),not(implies(X4,X3))),X2))),true),
    inference(congruence,[status(thm)],[c197]) ).

cnf(c199,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c200,plain,
    ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true) = ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true),
    inference(symmetry,[status(thm)],[c199]) ).

cnf(c201,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true) = is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c202,plain,
    is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))) = ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true),
    inference(symmetry,[status(thm)],[c201]) ).

cnf(c203,plain,
    is_a_theorem(implies(implies(implies(implies(not(X3),X3),X2),implies(X4,X2)),implies(implies(X3,X2),implies(X4,X2)))) = true,
    inference(substitution,[status(thm)],[c187]) ).

cnf(c204,plain,
    true = is_a_theorem(implies(implies(implies(implies(not(X3),X3),X2),implies(X4,X2)),implies(implies(X3,X2),implies(X4,X2)))),
    inference(symmetry,[status(thm)],[c203]) ).

cnf(c205,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true) = ifeq(is_a_theorem(implies(implies(implies(implies(not(X3),X3),X2),implies(X4,X2)),implies(implies(X3,X2),implies(X4,X2)))),true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true),
    inference(congruence,[status(thm)],[c204]) ).

cnf(c206,plain,
    ifeq(is_a_theorem(implies(implies(implies(implies(not(X3),X3),X2),implies(X4,X2)),implies(implies(X3,X2),implies(X4,X2)))),true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true) = true,
    inference(substitution,[status(thm)],[c113]) ).

cnf(c207,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true) = true,
    inference(transitivity,[status(thm)],[c205,c206]) ).

cnf(c208,plain,
    is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))) = true,
    inference(transitivity,[status(thm)],[c202,c207]) ).

cnf(c209,plain,
    true = is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),
    inference(symmetry,[status(thm)],[c208]) ).

cnf(c210,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = ifeq(is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true,ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true),
    inference(congruence,[status(thm)],[c209]) ).

cnf(c211,plain,
    ifeq(is_a_theorem(implies(implies(X4,implies(not(X3),X3)),implies(implies(X3,X2),implies(X4,X2)))),true,ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = true,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c212,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true),true) = true,
    inference(transitivity,[status(thm)],[c210,c211]) ).

cnf(c213,plain,
    ifeq(is_a_theorem(implies(X4,implies(not(X3),X3))),true,is_a_theorem(implies(implies(X3,X2),implies(X4,X2))),true) = true,
    inference(transitivity,[status(thm)],[c200,c212]) ).

cnf(c214,plain,
    ifeq(is_a_theorem(implies(implies(implies(X4,X3),not(implies(X4,X3))),implies(not(not(implies(X4,X3))),not(implies(X4,X3))))),true,is_a_theorem(implies(implies(not(implies(X4,X3)),X2),implies(implies(implies(X4,X3),not(implies(X4,X3))),X2))),true) = true,
    inference(substitution,[status(thm)],[c213]) ).

cnf(c215,plain,
    ifeq(true,true,is_a_theorem(implies(implies(not(implies(X4,X3)),X2),implies(implies(implies(X4,X3),not(implies(X4,X3))),X2))),true) = true,
    inference(transitivity,[status(thm)],[c198,c214]) ).

cnf(c216,plain,
    is_a_theorem(implies(implies(not(implies(X4,X3)),X2),implies(implies(implies(X4,X3),not(implies(X4,X3))),X2))) = true,
    inference(transitivity,[status(thm)],[c18,c215]) ).

cnf(c217,plain,
    is_a_theorem(implies(implies(not(implies(X3,X2)),not(implies(X3,X2))),implies(implies(implies(X3,X2),not(implies(X3,X2))),not(implies(X3,X2))))) = true,
    inference(substitution,[status(thm)],[c216]) ).

cnf(c218,plain,
    true = is_a_theorem(implies(implies(not(implies(X3,X2)),not(implies(X3,X2))),implies(implies(implies(X3,X2),not(implies(X3,X2))),not(implies(X3,X2))))),
    inference(symmetry,[status(thm)],[c217]) ).

cnf(c219,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X3,X2),not(implies(X3,X2))),not(implies(X3,X2)))),true) = ifeq(is_a_theorem(implies(implies(not(implies(X3,X2)),not(implies(X3,X2))),implies(implies(implies(X3,X2),not(implies(X3,X2))),not(implies(X3,X2))))),true,is_a_theorem(implies(implies(implies(X3,X2),not(implies(X3,X2))),not(implies(X3,X2)))),true),
    inference(congruence,[status(thm)],[c218]) ).

cnf(c220,plain,
    ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c221,plain,
    is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
    inference(symmetry,[status(thm)],[c220]) ).

cnf(c222,plain,
    ifeq(is_a_theorem(implies(implies(X3,X3),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(X3,X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
    inference(congruence,[status(thm)],[c221]) ).

cnf(c223,plain,
    ifeq(true,true,is_a_theorem(implies(X2,X2)),true) = is_a_theorem(implies(X2,X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c224,plain,
    is_a_theorem(implies(X2,X2)) = ifeq(true,true,is_a_theorem(implies(X2,X2)),true),
    inference(symmetry,[status(thm)],[c223]) ).

cnf(c225,plain,
    is_a_theorem(implies(implies(implies(not(X2),X2),X2),implies(X2,X2))) = true,
    inference(substitution,[status(thm)],[c74]) ).

cnf(c226,plain,
    true = is_a_theorem(implies(implies(implies(not(X2),X2),X2),implies(X2,X2))),
    inference(symmetry,[status(thm)],[c225]) ).

cnf(c227,plain,
    ifeq(true,true,is_a_theorem(implies(X2,X2)),true) = ifeq(is_a_theorem(implies(implies(implies(not(X2),X2),X2),implies(X2,X2))),true,is_a_theorem(implies(X2,X2)),true),
    inference(congruence,[status(thm)],[c226]) ).

cnf(c228,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(X2),X2),X2),implies(X2,X2))),true,is_a_theorem(implies(X2,X2)),true) = true,
    inference(substitution,[status(thm)],[c47]) ).

cnf(c229,plain,
    ifeq(true,true,is_a_theorem(implies(X2,X2)),true) = true,
    inference(transitivity,[status(thm)],[c227,c228]) ).

cnf(c230,plain,
    is_a_theorem(implies(X2,X2)) = true,
    inference(transitivity,[status(thm)],[c224,c229]) ).

cnf(c231,plain,
    true = is_a_theorem(implies(X2,X2)),
    inference(symmetry,[status(thm)],[c230]) ).

cnf(c232,plain,
    ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(X3,X3)),true,is_a_theorem(X2),true),
    inference(congruence,[status(thm)],[c231]) ).

cnf(c233,plain,
    ifeq(is_a_theorem(implies(implies(X3,X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(implies(implies(X3,X3),X2)),true,ifeq(is_a_theorem(implies(X3,X3)),true,is_a_theorem(X2),true),true),
    inference(congruence,[status(thm)],[c232]) ).

cnf(c234,plain,
    ifeq(is_a_theorem(implies(implies(X3,X3),X2)),true,ifeq(is_a_theorem(implies(X3,X3)),true,is_a_theorem(X2),true),true) = true,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c235,plain,
    ifeq(is_a_theorem(implies(implies(X3,X3),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
    inference(transitivity,[status(thm)],[c233,c234]) ).

cnf(c236,plain,
    ifeq(is_a_theorem(implies(implies(X3,X3),X2)),true,is_a_theorem(X2),true) = true,
    inference(transitivity,[status(thm)],[c222,c235]) ).

cnf(c237,plain,
    ifeq(is_a_theorem(implies(implies(not(implies(X3,X2)),not(implies(X3,X2))),implies(implies(implies(X3,X2),not(implies(X3,X2))),not(implies(X3,X2))))),true,is_a_theorem(implies(implies(implies(X3,X2),not(implies(X3,X2))),not(implies(X3,X2)))),true) = true,
    inference(substitution,[status(thm)],[c236]) ).

cnf(c238,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X3,X2),not(implies(X3,X2))),not(implies(X3,X2)))),true) = true,
    inference(transitivity,[status(thm)],[c219,c237]) ).

cnf(c239,plain,
    is_a_theorem(implies(implies(implies(X3,X2),not(implies(X3,X2))),not(implies(X3,X2)))) = true,
    inference(transitivity,[status(thm)],[c16,c238]) ).

cnf(c240,plain,
    is_a_theorem(implies(implies(implies(not(not(X2)),not(X2)),not(implies(not(not(X2)),not(X2)))),not(implies(not(not(X2)),not(X2))))) = true,
    inference(substitution,[status(thm)],[c239]) ).

cnf(c241,plain,
    true = is_a_theorem(implies(implies(implies(not(not(X2)),not(X2)),not(implies(not(not(X2)),not(X2)))),not(implies(not(not(X2)),not(X2))))),
    inference(symmetry,[status(thm)],[c240]) ).

cnf(c242,plain,
    ifeq(true,true,is_a_theorem(implies(X2,not(implies(not(not(X2)),not(X2))))),true) = ifeq(is_a_theorem(implies(implies(implies(not(not(X2)),not(X2)),not(implies(not(not(X2)),not(X2)))),not(implies(not(not(X2)),not(X2))))),true,is_a_theorem(implies(X2,not(implies(not(not(X2)),not(X2))))),true),
    inference(congruence,[status(thm)],[c241]) ).

cnf(c243,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(not(not(X4)),not(X4)),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(not(not(X4)),not(X4)),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c244,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(not(X4)),not(X4)),X3),X2)),true,is_a_theorem(implies(X4,X2)),true) = ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(not(not(X4)),not(X4)),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true),
    inference(symmetry,[status(thm)],[c243]) ).

cnf(c245,plain,
    true = is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))),
    inference(symmetry,[status(thm)],[c95]) ).

cnf(c246,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(not(not(X4)),not(X4)),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = ifeq(is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))),true,ifeq(is_a_theorem(implies(implies(implies(not(not(X4)),not(X4)),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true),
    inference(congruence,[status(thm)],[c245]) ).

cnf(c247,plain,
    ifeq(is_a_theorem(implies(implies(implies(implies(not(not(X4)),not(X4)),X3),X2),implies(X4,X2))),true,ifeq(is_a_theorem(implies(implies(implies(not(not(X4)),not(X4)),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = true,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c248,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(not(not(X4)),not(X4)),X3),X2)),true,is_a_theorem(implies(X4,X2)),true),true) = true,
    inference(transitivity,[status(thm)],[c246,c247]) ).

cnf(c249,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(not(X4)),not(X4)),X3),X2)),true,is_a_theorem(implies(X4,X2)),true) = true,
    inference(transitivity,[status(thm)],[c244,c248]) ).

cnf(c250,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(not(X2)),not(X2)),not(implies(not(not(X2)),not(X2)))),not(implies(not(not(X2)),not(X2))))),true,is_a_theorem(implies(X2,not(implies(not(not(X2)),not(X2))))),true) = true,
    inference(substitution,[status(thm)],[c249]) ).

cnf(c251,plain,
    ifeq(true,true,is_a_theorem(implies(X2,not(implies(not(not(X2)),not(X2))))),true) = true,
    inference(transitivity,[status(thm)],[c242,c250]) ).

cnf(c252,plain,
    is_a_theorem(implies(X2,not(implies(not(not(X2)),not(X2))))) = true,
    inference(transitivity,[status(thm)],[c14,c251]) ).

cnf(c253,plain,
    true = is_a_theorem(implies(X2,not(implies(not(not(X2)),not(X2))))),
    inference(symmetry,[status(thm)],[c252]) ).

cnf(c254,plain,
    ifeq(true,true,is_a_theorem(implies(implies(not(not(X3)),not(X3)),implies(X3,X2))),true) = ifeq(is_a_theorem(implies(X3,not(implies(not(not(X3)),not(X3))))),true,is_a_theorem(implies(implies(not(not(X3)),not(X3)),implies(X3,X2))),true),
    inference(congruence,[status(thm)],[c253]) ).

cnf(c255,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(X4,not(X3))),true,is_a_theorem(implies(X3,implies(X4,X2))),true),true) = ifeq(is_a_theorem(implies(X4,not(X3))),true,is_a_theorem(implies(X3,implies(X4,X2))),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c256,plain,
    ifeq(is_a_theorem(implies(X4,not(X3))),true,is_a_theorem(implies(X3,implies(X4,X2))),true) = ifeq(true,true,ifeq(is_a_theorem(implies(X4,not(X3))),true,is_a_theorem(implies(X3,implies(X4,X2))),true),true),
    inference(symmetry,[status(thm)],[c255]) ).

cnf(c257,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X4,not(X3)),implies(X3,implies(X4,X2)))),true) = is_a_theorem(implies(implies(X4,not(X3)),implies(X3,implies(X4,X2)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c258,plain,
    is_a_theorem(implies(implies(X4,not(X3)),implies(X3,implies(X4,X2)))) = ifeq(true,true,is_a_theorem(implies(implies(X4,not(X3)),implies(X3,implies(X4,X2)))),true),
    inference(symmetry,[status(thm)],[c257]) ).

cnf(c259,plain,
    is_a_theorem(implies(implies(implies(implies(not(X3),X2),implies(X4,X2)),implies(X3,implies(X4,X2))),implies(implies(X4,not(X3)),implies(X3,implies(X4,X2))))) = true,
    inference(substitution,[status(thm)],[c108]) ).

cnf(c260,plain,
    true = is_a_theorem(implies(implies(implies(implies(not(X3),X2),implies(X4,X2)),implies(X3,implies(X4,X2))),implies(implies(X4,not(X3)),implies(X3,implies(X4,X2))))),
    inference(symmetry,[status(thm)],[c259]) ).

cnf(c261,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X4,not(X3)),implies(X3,implies(X4,X2)))),true) = ifeq(is_a_theorem(implies(implies(implies(implies(not(X3),X2),implies(X4,X2)),implies(X3,implies(X4,X2))),implies(implies(X4,not(X3)),implies(X3,implies(X4,X2))))),true,is_a_theorem(implies(implies(X4,not(X3)),implies(X3,implies(X4,X2)))),true),
    inference(congruence,[status(thm)],[c260]) ).

cnf(c262,plain,
    ifeq(is_a_theorem(implies(implies(implies(implies(not(X3),X2),implies(X4,X2)),implies(X3,implies(X4,X2))),implies(implies(X4,not(X3)),implies(X3,implies(X4,X2))))),true,is_a_theorem(implies(implies(X4,not(X3)),implies(X3,implies(X4,X2)))),true) = true,
    inference(substitution,[status(thm)],[c153]) ).

cnf(c263,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X4,not(X3)),implies(X3,implies(X4,X2)))),true) = true,
    inference(transitivity,[status(thm)],[c261,c262]) ).

cnf(c264,plain,
    is_a_theorem(implies(implies(X4,not(X3)),implies(X3,implies(X4,X2)))) = true,
    inference(transitivity,[status(thm)],[c258,c263]) ).

cnf(c265,plain,
    true = is_a_theorem(implies(implies(X4,not(X3)),implies(X3,implies(X4,X2)))),
    inference(symmetry,[status(thm)],[c264]) ).

cnf(c266,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(X4,not(X3))),true,is_a_theorem(implies(X3,implies(X4,X2))),true),true) = ifeq(is_a_theorem(implies(implies(X4,not(X3)),implies(X3,implies(X4,X2)))),true,ifeq(is_a_theorem(implies(X4,not(X3))),true,is_a_theorem(implies(X3,implies(X4,X2))),true),true),
    inference(congruence,[status(thm)],[c265]) ).

cnf(c267,plain,
    ifeq(is_a_theorem(implies(implies(X4,not(X3)),implies(X3,implies(X4,X2)))),true,ifeq(is_a_theorem(implies(X4,not(X3))),true,is_a_theorem(implies(X3,implies(X4,X2))),true),true) = true,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c268,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(X4,not(X3))),true,is_a_theorem(implies(X3,implies(X4,X2))),true),true) = true,
    inference(transitivity,[status(thm)],[c266,c267]) ).

cnf(c269,plain,
    ifeq(is_a_theorem(implies(X4,not(X3))),true,is_a_theorem(implies(X3,implies(X4,X2))),true) = true,
    inference(transitivity,[status(thm)],[c256,c268]) ).

cnf(c270,plain,
    ifeq(is_a_theorem(implies(X3,not(implies(not(not(X3)),not(X3))))),true,is_a_theorem(implies(implies(not(not(X3)),not(X3)),implies(X3,X2))),true) = true,
    inference(substitution,[status(thm)],[c269]) ).

cnf(c271,plain,
    ifeq(true,true,is_a_theorem(implies(implies(not(not(X3)),not(X3)),implies(X3,X2))),true) = true,
    inference(transitivity,[status(thm)],[c254,c270]) ).

cnf(c272,plain,
    is_a_theorem(implies(implies(not(not(X3)),not(X3)),implies(X3,X2))) = true,
    inference(transitivity,[status(thm)],[c12,c271]) ).

cnf(c273,plain,
    true = is_a_theorem(implies(implies(not(not(X3)),not(X3)),implies(X3,X2))),
    inference(symmetry,[status(thm)],[c272]) ).

cnf(c274,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X4,X3),X2),implies(not(X4),X2))),true) = ifeq(is_a_theorem(implies(implies(not(not(X4)),not(X4)),implies(X4,X3))),true,is_a_theorem(implies(implies(implies(X4,X3),X2),implies(not(X4),X2))),true),
    inference(congruence,[status(thm)],[c273]) ).

cnf(c275,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X5),X4),X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X5,X2))),true),true) = ifeq(is_a_theorem(implies(implies(not(X5),X4),X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X5,X2))),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c276,plain,
    ifeq(is_a_theorem(implies(implies(not(X5),X4),X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X5,X2))),true) = ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X5),X4),X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X5,X2))),true),true),
    inference(symmetry,[status(thm)],[c275]) ).

cnf(c277,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(not(X5),X4),X3),implies(implies(X3,X2),implies(X5,X2)))),true) = is_a_theorem(implies(implies(implies(not(X5),X4),X3),implies(implies(X3,X2),implies(X5,X2)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c278,plain,
    is_a_theorem(implies(implies(implies(not(X5),X4),X3),implies(implies(X3,X2),implies(X5,X2)))) = ifeq(true,true,is_a_theorem(implies(implies(implies(not(X5),X4),X3),implies(implies(X3,X2),implies(X5,X2)))),true),
    inference(symmetry,[status(thm)],[c277]) ).

cnf(c279,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X5,X4),X3),implies(implies(implies(not(X5),X2),X4),X3))),true) = is_a_theorem(implies(implies(implies(X5,X4),X3),implies(implies(implies(not(X5),X2),X4),X3))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c280,plain,
    is_a_theorem(implies(implies(implies(X5,X4),X3),implies(implies(implies(not(X5),X2),X4),X3))) = ifeq(true,true,is_a_theorem(implies(implies(implies(X5,X4),X3),implies(implies(implies(not(X5),X2),X4),X3))),true),
    inference(symmetry,[status(thm)],[c279]) ).

cnf(c281,plain,
    is_a_theorem(implies(implies(implies(not(X4),X2),X3),implies(X4,X3))) = true,
    inference(substitution,[status(thm)],[c74]) ).

cnf(c282,plain,
    true = is_a_theorem(implies(implies(implies(not(X4),X2),X3),implies(X4,X3))),
    inference(symmetry,[status(thm)],[c281]) ).

cnf(c283,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X5,X4),X3),implies(implies(implies(not(X5),X2),X4),X3))),true) = ifeq(is_a_theorem(implies(implies(implies(not(X5),X2),X4),implies(X5,X4))),true,is_a_theorem(implies(implies(implies(X5,X4),X3),implies(implies(implies(not(X5),X2),X4),X3))),true),
    inference(congruence,[status(thm)],[c282]) ).

cnf(c284,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(X5),X2),X4),implies(X5,X4))),true,is_a_theorem(implies(implies(implies(X5,X4),X3),implies(implies(implies(not(X5),X2),X4),X3))),true) = true,
    inference(substitution,[status(thm)],[c92]) ).

cnf(c285,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X5,X4),X3),implies(implies(implies(not(X5),X2),X4),X3))),true) = true,
    inference(transitivity,[status(thm)],[c283,c284]) ).

cnf(c286,plain,
    is_a_theorem(implies(implies(implies(X5,X4),X3),implies(implies(implies(not(X5),X2),X4),X3))) = true,
    inference(transitivity,[status(thm)],[c280,c285]) ).

cnf(c287,plain,
    is_a_theorem(implies(implies(implies(X5,X3),implies(implies(X3,X2),implies(X5,X2))),implies(implies(implies(not(X5),X4),X3),implies(implies(X3,X2),implies(X5,X2))))) = true,
    inference(substitution,[status(thm)],[c286]) ).

cnf(c288,plain,
    true = is_a_theorem(implies(implies(implies(X5,X3),implies(implies(X3,X2),implies(X5,X2))),implies(implies(implies(not(X5),X4),X3),implies(implies(X3,X2),implies(X5,X2))))),
    inference(symmetry,[status(thm)],[c287]) ).

cnf(c289,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(not(X5),X4),X3),implies(implies(X3,X2),implies(X5,X2)))),true) = ifeq(is_a_theorem(implies(implies(implies(X5,X3),implies(implies(X3,X2),implies(X5,X2))),implies(implies(implies(not(X5),X4),X3),implies(implies(X3,X2),implies(X5,X2))))),true,is_a_theorem(implies(implies(implies(not(X5),X4),X3),implies(implies(X3,X2),implies(X5,X2)))),true),
    inference(congruence,[status(thm)],[c288]) ).

cnf(c290,plain,
    ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c291,plain,
    is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
    inference(symmetry,[status(thm)],[c290]) ).

cnf(c292,plain,
    ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(implies(X4,X3),implies(X5,X3))),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(implies(X4,X3),implies(X5,X3))),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
    inference(congruence,[status(thm)],[c291]) ).

cnf(c293,plain,
    is_a_theorem(implies(implies(X4,X3),implies(implies(X3,X2),implies(X4,X2)))) = true,
    inference(substitution,[status(thm)],[c33]) ).

cnf(c294,plain,
    true = is_a_theorem(implies(implies(X4,X3),implies(implies(X3,X2),implies(X4,X2)))),
    inference(symmetry,[status(thm)],[c293]) ).

cnf(c295,plain,
    ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(X5,X4),implies(implies(X4,X3),implies(X5,X3)))),true,is_a_theorem(X2),true),
    inference(congruence,[status(thm)],[c294]) ).

cnf(c296,plain,
    ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(implies(X4,X3),implies(X5,X3))),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(implies(X4,X3),implies(X5,X3))),X2)),true,ifeq(is_a_theorem(implies(implies(X5,X4),implies(implies(X4,X3),implies(X5,X3)))),true,is_a_theorem(X2),true),true),
    inference(congruence,[status(thm)],[c295]) ).

cnf(c297,plain,
    ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(implies(X4,X3),implies(X5,X3))),X2)),true,ifeq(is_a_theorem(implies(implies(X5,X4),implies(implies(X4,X3),implies(X5,X3)))),true,is_a_theorem(X2),true),true) = true,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c298,plain,
    ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(implies(X4,X3),implies(X5,X3))),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
    inference(transitivity,[status(thm)],[c296,c297]) ).

cnf(c299,plain,
    ifeq(is_a_theorem(implies(implies(implies(X5,X4),implies(implies(X4,X3),implies(X5,X3))),X2)),true,is_a_theorem(X2),true) = true,
    inference(transitivity,[status(thm)],[c292,c298]) ).

cnf(c300,plain,
    ifeq(is_a_theorem(implies(implies(implies(X5,X3),implies(implies(X3,X2),implies(X5,X2))),implies(implies(implies(not(X5),X4),X3),implies(implies(X3,X2),implies(X5,X2))))),true,is_a_theorem(implies(implies(implies(not(X5),X4),X3),implies(implies(X3,X2),implies(X5,X2)))),true) = true,
    inference(substitution,[status(thm)],[c299]) ).

cnf(c301,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(not(X5),X4),X3),implies(implies(X3,X2),implies(X5,X2)))),true) = true,
    inference(transitivity,[status(thm)],[c289,c300]) ).

cnf(c302,plain,
    is_a_theorem(implies(implies(implies(not(X5),X4),X3),implies(implies(X3,X2),implies(X5,X2)))) = true,
    inference(transitivity,[status(thm)],[c278,c301]) ).

cnf(c303,plain,
    true = is_a_theorem(implies(implies(implies(not(X5),X4),X3),implies(implies(X3,X2),implies(X5,X2)))),
    inference(symmetry,[status(thm)],[c302]) ).

cnf(c304,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X5),X4),X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X5,X2))),true),true) = ifeq(is_a_theorem(implies(implies(implies(not(X5),X4),X3),implies(implies(X3,X2),implies(X5,X2)))),true,ifeq(is_a_theorem(implies(implies(not(X5),X4),X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X5,X2))),true),true),
    inference(congruence,[status(thm)],[c303]) ).

cnf(c305,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(X5),X4),X3),implies(implies(X3,X2),implies(X5,X2)))),true,ifeq(is_a_theorem(implies(implies(not(X5),X4),X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X5,X2))),true),true) = true,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c306,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(X5),X4),X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X5,X2))),true),true) = true,
    inference(transitivity,[status(thm)],[c304,c305]) ).

cnf(c307,plain,
    ifeq(is_a_theorem(implies(implies(not(X5),X4),X3)),true,is_a_theorem(implies(implies(X3,X2),implies(X5,X2))),true) = true,
    inference(transitivity,[status(thm)],[c276,c306]) ).

cnf(c308,plain,
    ifeq(is_a_theorem(implies(implies(not(not(X4)),not(X4)),implies(X4,X3))),true,is_a_theorem(implies(implies(implies(X4,X3),X2),implies(not(X4),X2))),true) = true,
    inference(substitution,[status(thm)],[c307]) ).

cnf(c309,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X4,X3),X2),implies(not(X4),X2))),true) = true,
    inference(transitivity,[status(thm)],[c274,c308]) ).

cnf(c310,plain,
    is_a_theorem(implies(implies(implies(X4,X3),X2),implies(not(X4),X2))) = true,
    inference(transitivity,[status(thm)],[c10,c309]) ).

cnf(c311,plain,
    is_a_theorem(implies(implies(implies(X3,X2),implies(X4,X2)),implies(not(X3),implies(X4,X2)))) = true,
    inference(substitution,[status(thm)],[c310]) ).

cnf(c312,plain,
    true = is_a_theorem(implies(implies(implies(X3,X2),implies(X4,X2)),implies(not(X3),implies(X4,X2)))),
    inference(symmetry,[status(thm)],[c311]) ).

cnf(c313,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(not(X3),implies(X4,X2)))),true) = ifeq(is_a_theorem(implies(implies(implies(X3,X2),implies(X4,X2)),implies(not(X3),implies(X4,X2)))),true,is_a_theorem(implies(implies(X4,X3),implies(not(X3),implies(X4,X2)))),true),
    inference(congruence,[status(thm)],[c312]) ).

cnf(c314,plain,
    ifeq(is_a_theorem(implies(implies(implies(X3,X2),implies(X4,X2)),implies(not(X3),implies(X4,X2)))),true,is_a_theorem(implies(implies(X4,X3),implies(not(X3),implies(X4,X2)))),true) = true,
    inference(substitution,[status(thm)],[c113]) ).

cnf(c315,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(not(X3),implies(X4,X2)))),true) = true,
    inference(transitivity,[status(thm)],[c313,c314]) ).

cnf(c316,plain,
    is_a_theorem(implies(implies(X4,X3),implies(not(X3),implies(X4,X2)))) = true,
    inference(transitivity,[status(thm)],[c8,c315]) ).

cnf(c317,plain,
    is_a_theorem(implies(implies(X3,implies(X4,X3)),implies(not(implies(X4,X3)),implies(X3,X2)))) = true,
    inference(substitution,[status(thm)],[c316]) ).

cnf(c318,plain,
    true = is_a_theorem(implies(implies(X3,implies(X4,X3)),implies(not(implies(X4,X3)),implies(X3,X2)))),
    inference(symmetry,[status(thm)],[c317]) ).

cnf(c319,plain,
    ifeq(true,true,is_a_theorem(implies(not(implies(X4,X3)),implies(X3,X2))),true) = ifeq(is_a_theorem(implies(implies(X3,implies(X4,X3)),implies(not(implies(X4,X3)),implies(X3,X2)))),true,is_a_theorem(implies(not(implies(X4,X3)),implies(X3,X2))),true),
    inference(congruence,[status(thm)],[c318]) ).

cnf(c320,plain,
    ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c321,plain,
    is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
    inference(symmetry,[status(thm)],[c320]) ).

cnf(c322,plain,
    ifeq(is_a_theorem(implies(implies(X4,implies(X3,X4)),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(X4,implies(X3,X4)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
    inference(congruence,[status(thm)],[c321]) ).

cnf(c323,plain,
    ifeq(true,true,is_a_theorem(implies(X3,implies(X2,X3))),true) = is_a_theorem(implies(X3,implies(X2,X3))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c324,plain,
    is_a_theorem(implies(X3,implies(X2,X3))) = ifeq(true,true,is_a_theorem(implies(X3,implies(X2,X3))),true),
    inference(symmetry,[status(thm)],[c323]) ).

cnf(c325,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(X3,X2))),true) = is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(X3,X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c326,plain,
    is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(X3,X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(X3,X2))),true),
    inference(symmetry,[status(thm)],[c325]) ).

cnf(c327,plain,
    ifeq(true,true,is_a_theorem(implies(X4,implies(X3,implies(X2,X4)))),true) = is_a_theorem(implies(X4,implies(X3,implies(X2,X4)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c328,plain,
    is_a_theorem(implies(X4,implies(X3,implies(X2,X4)))) = ifeq(true,true,is_a_theorem(implies(X4,implies(X3,implies(X2,X4)))),true),
    inference(symmetry,[status(thm)],[c327]) ).

cnf(c329,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X4,implies(X5,implies(X2,X3))))),true) = is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X4,implies(X5,implies(X2,X3))))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c330,plain,
    is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X4,implies(X5,implies(X2,X3))))) = ifeq(true,true,is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X4,implies(X5,implies(X2,X3))))),true),
    inference(symmetry,[status(thm)],[c329]) ).

cnf(c331,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(X5,X2))),true) = is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(X5,X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c332,plain,
    is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(X5,X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(X5,X2))),true),
    inference(symmetry,[status(thm)],[c331]) ).

cnf(c333,plain,
    ifeq(true,true,is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))),true) = is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c334,plain,
    is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))) = ifeq(true,true,is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))),true),
    inference(symmetry,[status(thm)],[c333]) ).

cnf(c335,plain,
    is_a_theorem(implies(implies(X2,implies(not(X4),X4)),implies(implies(X4,X3),implies(X2,X3)))) = true,
    inference(substitution,[status(thm)],[c208]) ).

cnf(c336,plain,
    true = is_a_theorem(implies(implies(X2,implies(not(X4),X4)),implies(implies(X4,X3),implies(X2,X3)))),
    inference(symmetry,[status(thm)],[c335]) ).

cnf(c337,plain,
    ifeq(true,true,is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))),true) = ifeq(is_a_theorem(implies(implies(X2,implies(not(X4),X4)),implies(implies(X4,X3),implies(X2,X3)))),true,is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))),true),
    inference(congruence,[status(thm)],[c336]) ).

cnf(c338,plain,
    ifeq(is_a_theorem(implies(implies(X2,implies(not(X4),X4)),implies(implies(X4,X3),implies(X2,X3)))),true,is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))),true) = true,
    inference(substitution,[status(thm)],[c167]) ).

cnf(c339,plain,
    ifeq(true,true,is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))),true) = true,
    inference(transitivity,[status(thm)],[c337,c338]) ).

cnf(c340,plain,
    is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))) = true,
    inference(transitivity,[status(thm)],[c334,c339]) ).

cnf(c341,plain,
    true = is_a_theorem(implies(X4,implies(implies(X4,X3),implies(X2,X3)))),
    inference(symmetry,[status(thm)],[c340]) ).

cnf(c342,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(X5,X2))),true) = ifeq(is_a_theorem(implies(X5,implies(implies(X5,X4),implies(X3,X4)))),true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(X5,X2))),true),
    inference(congruence,[status(thm)],[c341]) ).

cnf(c343,plain,
    ifeq(is_a_theorem(implies(X5,implies(implies(X5,X4),implies(X3,X4)))),true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(X5,X2))),true) = true,
    inference(substitution,[status(thm)],[c92]) ).

cnf(c344,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(X5,X2))),true) = true,
    inference(transitivity,[status(thm)],[c342,c343]) ).

cnf(c345,plain,
    is_a_theorem(implies(implies(implies(implies(X5,X4),implies(X3,X4)),X2),implies(X5,X2))) = true,
    inference(transitivity,[status(thm)],[c332,c344]) ).

cnf(c346,plain,
    is_a_theorem(implies(implies(implies(implies(X4,X3),implies(X2,X3)),implies(X5,implies(X2,X3))),implies(X4,implies(X5,implies(X2,X3))))) = true,
    inference(substitution,[status(thm)],[c345]) ).

cnf(c347,plain,
    true = is_a_theorem(implies(implies(implies(implies(X4,X3),implies(X2,X3)),implies(X5,implies(X2,X3))),implies(X4,implies(X5,implies(X2,X3))))),
    inference(symmetry,[status(thm)],[c346]) ).

cnf(c348,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X4,implies(X5,implies(X2,X3))))),true) = ifeq(is_a_theorem(implies(implies(implies(implies(X4,X3),implies(X2,X3)),implies(X5,implies(X2,X3))),implies(X4,implies(X5,implies(X2,X3))))),true,is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X4,implies(X5,implies(X2,X3))))),true),
    inference(congruence,[status(thm)],[c347]) ).

cnf(c349,plain,
    ifeq(is_a_theorem(implies(implies(implies(implies(X4,X3),implies(X2,X3)),implies(X5,implies(X2,X3))),implies(X4,implies(X5,implies(X2,X3))))),true,is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X4,implies(X5,implies(X2,X3))))),true) = true,
    inference(substitution,[status(thm)],[c113]) ).

cnf(c350,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X4,implies(X5,implies(X2,X3))))),true) = true,
    inference(transitivity,[status(thm)],[c348,c349]) ).

cnf(c351,plain,
    is_a_theorem(implies(implies(X5,implies(X4,X3)),implies(X4,implies(X5,implies(X2,X3))))) = true,
    inference(transitivity,[status(thm)],[c330,c350]) ).

cnf(c352,plain,
    is_a_theorem(implies(implies(X3,implies(X4,X4)),implies(X4,implies(X3,implies(X2,X4))))) = true,
    inference(substitution,[status(thm)],[c351]) ).

cnf(c353,plain,
    true = is_a_theorem(implies(implies(X3,implies(X4,X4)),implies(X4,implies(X3,implies(X2,X4))))),
    inference(symmetry,[status(thm)],[c352]) ).

cnf(c354,plain,
    ifeq(true,true,is_a_theorem(implies(X4,implies(X3,implies(X2,X4)))),true) = ifeq(is_a_theorem(implies(implies(X3,implies(X4,X4)),implies(X4,implies(X3,implies(X2,X4))))),true,is_a_theorem(implies(X4,implies(X3,implies(X2,X4)))),true),
    inference(congruence,[status(thm)],[c353]) ).

cnf(c355,plain,
    ifeq(true,true,is_a_theorem(X2),true) = is_a_theorem(X2),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c356,plain,
    is_a_theorem(X2) = ifeq(true,true,is_a_theorem(X2),true),
    inference(symmetry,[status(thm)],[c355]) ).

cnf(c357,plain,
    ifeq(is_a_theorem(implies(implies(X4,implies(X3,X3)),X2)),true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(implies(X4,implies(X3,X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true),
    inference(congruence,[status(thm)],[c356]) ).

cnf(c358,plain,
    ifeq(true,true,is_a_theorem(implies(X3,implies(X2,X2))),true) = is_a_theorem(implies(X3,implies(X2,X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c359,plain,
    is_a_theorem(implies(X3,implies(X2,X2))) = ifeq(true,true,is_a_theorem(implies(X3,implies(X2,X2))),true),
    inference(symmetry,[status(thm)],[c358]) ).

cnf(c360,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(X5,X5)),X4),X3),implies(X2,X3))),true) = is_a_theorem(implies(implies(implies(not(implies(X5,X5)),X4),X3),implies(X2,X3))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c361,plain,
    is_a_theorem(implies(implies(implies(not(implies(X5,X5)),X4),X3),implies(X2,X3))) = ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(X5,X5)),X4),X3),implies(X2,X3))),true),
    inference(symmetry,[status(thm)],[c360]) ).

cnf(c362,plain,
    ifeq(true,true,is_a_theorem(implies(X4,implies(not(implies(X3,X3)),X2))),true) = is_a_theorem(implies(X4,implies(not(implies(X3,X3)),X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c363,plain,
    is_a_theorem(implies(X4,implies(not(implies(X3,X3)),X2))) = ifeq(true,true,is_a_theorem(implies(X4,implies(not(implies(X3,X3)),X2))),true),
    inference(symmetry,[status(thm)],[c362]) ).

cnf(c364,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(not(implies(X2,X2)),X3))),true) = is_a_theorem(implies(implies(X4,X3),implies(not(implies(X2,X2)),X3))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c365,plain,
    is_a_theorem(implies(implies(X4,X3),implies(not(implies(X2,X2)),X3))) = ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(not(implies(X2,X2)),X3))),true),
    inference(symmetry,[status(thm)],[c364]) ).

cnf(c366,plain,
    ifeq(true,true,is_a_theorem(implies(not(implies(X3,X3)),X2)),true) = is_a_theorem(implies(not(implies(X3,X3)),X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c367,plain,
    is_a_theorem(implies(not(implies(X3,X3)),X2)) = ifeq(true,true,is_a_theorem(implies(not(implies(X3,X3)),X2)),true),
    inference(symmetry,[status(thm)],[c366]) ).

cnf(c368,plain,
    true = is_a_theorem(implies(X2,X2)),
    inference(symmetry,[status(thm)],[c230]) ).

cnf(c369,plain,
    ifeq(true,true,is_a_theorem(implies(not(implies(X3,X3)),X2)),true) = ifeq(is_a_theorem(implies(X3,X3)),true,is_a_theorem(implies(not(implies(X3,X3)),X2)),true),
    inference(congruence,[status(thm)],[c368]) ).

cnf(c370,plain,
    ifeq(true,true,ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),true) = ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c371,plain,
    ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true) = ifeq(true,true,ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),true),
    inference(symmetry,[status(thm)],[c370]) ).

cnf(c372,plain,
    is_a_theorem(implies(X3,implies(not(X3),X2))) = true,
    inference(substitution,[status(thm)],[c64]) ).

cnf(c373,plain,
    true = is_a_theorem(implies(X3,implies(not(X3),X2))),
    inference(symmetry,[status(thm)],[c372]) ).

cnf(c374,plain,
    ifeq(true,true,ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),true) = ifeq(is_a_theorem(implies(X3,implies(not(X3),X2))),true,ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),true),
    inference(congruence,[status(thm)],[c373]) ).

cnf(c375,plain,
    ifeq(is_a_theorem(implies(X3,implies(not(X3),X2))),true,ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),true) = true,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c376,plain,
    ifeq(true,true,ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true),true) = true,
    inference(transitivity,[status(thm)],[c374,c375]) ).

cnf(c377,plain,
    ifeq(is_a_theorem(X3),true,is_a_theorem(implies(not(X3),X2)),true) = true,
    inference(transitivity,[status(thm)],[c371,c376]) ).

cnf(c378,plain,
    ifeq(is_a_theorem(implies(X3,X3)),true,is_a_theorem(implies(not(implies(X3,X3)),X2)),true) = true,
    inference(substitution,[status(thm)],[c377]) ).

cnf(c379,plain,
    ifeq(true,true,is_a_theorem(implies(not(implies(X3,X3)),X2)),true) = true,
    inference(transitivity,[status(thm)],[c369,c378]) ).

cnf(c380,plain,
    is_a_theorem(implies(not(implies(X3,X3)),X2)) = true,
    inference(transitivity,[status(thm)],[c367,c379]) ).

cnf(c381,plain,
    is_a_theorem(implies(not(implies(X2,X2)),X3)) = true,
    inference(substitution,[status(thm)],[c380]) ).

cnf(c382,plain,
    true = is_a_theorem(implies(not(implies(X2,X2)),X3)),
    inference(symmetry,[status(thm)],[c381]) ).

cnf(c383,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(not(implies(X2,X2)),X3))),true) = ifeq(is_a_theorem(implies(not(implies(X2,X2)),X4)),true,is_a_theorem(implies(implies(X4,X3),implies(not(implies(X2,X2)),X3))),true),
    inference(congruence,[status(thm)],[c382]) ).

cnf(c384,plain,
    ifeq(is_a_theorem(implies(not(implies(X2,X2)),X4)),true,is_a_theorem(implies(implies(X4,X3),implies(not(implies(X2,X2)),X3))),true) = true,
    inference(substitution,[status(thm)],[c92]) ).

cnf(c385,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X4,X3),implies(not(implies(X2,X2)),X3))),true) = true,
    inference(transitivity,[status(thm)],[c383,c384]) ).

cnf(c386,plain,
    is_a_theorem(implies(implies(X4,X3),implies(not(implies(X2,X2)),X3))) = true,
    inference(transitivity,[status(thm)],[c365,c385]) ).

cnf(c387,plain,
    is_a_theorem(implies(implies(not(X4),X2),implies(not(implies(X3,X3)),X2))) = true,
    inference(substitution,[status(thm)],[c386]) ).

cnf(c388,plain,
    true = is_a_theorem(implies(implies(not(X4),X2),implies(not(implies(X3,X3)),X2))),
    inference(symmetry,[status(thm)],[c387]) ).

cnf(c389,plain,
    ifeq(true,true,is_a_theorem(implies(X4,implies(not(implies(X3,X3)),X2))),true) = ifeq(is_a_theorem(implies(implies(not(X4),X2),implies(not(implies(X3,X3)),X2))),true,is_a_theorem(implies(X4,implies(not(implies(X3,X3)),X2))),true),
    inference(congruence,[status(thm)],[c388]) ).

cnf(c390,plain,
    ifeq(is_a_theorem(implies(implies(not(X4),X2),implies(not(implies(X3,X3)),X2))),true,is_a_theorem(implies(X4,implies(not(implies(X3,X3)),X2))),true) = true,
    inference(substitution,[status(thm)],[c79]) ).

cnf(c391,plain,
    ifeq(true,true,is_a_theorem(implies(X4,implies(not(implies(X3,X3)),X2))),true) = true,
    inference(transitivity,[status(thm)],[c389,c390]) ).

cnf(c392,plain,
    is_a_theorem(implies(X4,implies(not(implies(X3,X3)),X2))) = true,
    inference(transitivity,[status(thm)],[c363,c391]) ).

cnf(c393,plain,
    is_a_theorem(implies(X2,implies(not(implies(X4,X4)),X3))) = true,
    inference(substitution,[status(thm)],[c392]) ).

cnf(c394,plain,
    true = is_a_theorem(implies(X2,implies(not(implies(X4,X4)),X3))),
    inference(symmetry,[status(thm)],[c393]) ).

cnf(c395,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(X5,X5)),X4),X3),implies(X2,X3))),true) = ifeq(is_a_theorem(implies(X2,implies(not(implies(X5,X5)),X4))),true,is_a_theorem(implies(implies(implies(not(implies(X5,X5)),X4),X3),implies(X2,X3))),true),
    inference(congruence,[status(thm)],[c394]) ).

cnf(c396,plain,
    ifeq(is_a_theorem(implies(X2,implies(not(implies(X5,X5)),X4))),true,is_a_theorem(implies(implies(implies(not(implies(X5,X5)),X4),X3),implies(X2,X3))),true) = true,
    inference(substitution,[status(thm)],[c92]) ).

cnf(c397,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(X5,X5)),X4),X3),implies(X2,X3))),true) = true,
    inference(transitivity,[status(thm)],[c395,c396]) ).

cnf(c398,plain,
    is_a_theorem(implies(implies(implies(not(implies(X5,X5)),X4),X3),implies(X2,X3))) = true,
    inference(transitivity,[status(thm)],[c361,c397]) ).

cnf(c399,plain,
    is_a_theorem(implies(implies(implies(not(implies(X2,X2)),implies(X2,X2)),implies(X2,X2)),implies(X3,implies(X2,X2)))) = true,
    inference(substitution,[status(thm)],[c398]) ).

cnf(c400,plain,
    true = is_a_theorem(implies(implies(implies(not(implies(X2,X2)),implies(X2,X2)),implies(X2,X2)),implies(X3,implies(X2,X2)))),
    inference(symmetry,[status(thm)],[c399]) ).

cnf(c401,plain,
    ifeq(true,true,is_a_theorem(implies(X3,implies(X2,X2))),true) = ifeq(is_a_theorem(implies(implies(implies(not(implies(X2,X2)),implies(X2,X2)),implies(X2,X2)),implies(X3,implies(X2,X2)))),true,is_a_theorem(implies(X3,implies(X2,X2))),true),
    inference(congruence,[status(thm)],[c400]) ).

cnf(c402,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(implies(X2,X2)),implies(X2,X2)),implies(X2,X2)),implies(X3,implies(X2,X2)))),true,is_a_theorem(implies(X3,implies(X2,X2))),true) = true,
    inference(substitution,[status(thm)],[c47]) ).

cnf(c403,plain,
    ifeq(true,true,is_a_theorem(implies(X3,implies(X2,X2))),true) = true,
    inference(transitivity,[status(thm)],[c401,c402]) ).

cnf(c404,plain,
    is_a_theorem(implies(X3,implies(X2,X2))) = true,
    inference(transitivity,[status(thm)],[c359,c403]) ).

cnf(c405,plain,
    true = is_a_theorem(implies(X3,implies(X2,X2))),
    inference(symmetry,[status(thm)],[c404]) ).

cnf(c406,plain,
    ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(X4,implies(X3,X3))),true,is_a_theorem(X2),true),
    inference(congruence,[status(thm)],[c405]) ).

cnf(c407,plain,
    ifeq(is_a_theorem(implies(implies(X4,implies(X3,X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(implies(implies(X4,implies(X3,X3)),X2)),true,ifeq(is_a_theorem(implies(X4,implies(X3,X3))),true,is_a_theorem(X2),true),true),
    inference(congruence,[status(thm)],[c406]) ).

cnf(c408,plain,
    ifeq(is_a_theorem(implies(implies(X4,implies(X3,X3)),X2)),true,ifeq(is_a_theorem(implies(X4,implies(X3,X3))),true,is_a_theorem(X2),true),true) = true,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c409,plain,
    ifeq(is_a_theorem(implies(implies(X4,implies(X3,X3)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
    inference(transitivity,[status(thm)],[c407,c408]) ).

cnf(c410,plain,
    ifeq(is_a_theorem(implies(implies(X4,implies(X3,X3)),X2)),true,is_a_theorem(X2),true) = true,
    inference(transitivity,[status(thm)],[c357,c409]) ).

cnf(c411,plain,
    ifeq(is_a_theorem(implies(implies(X3,implies(X4,X4)),implies(X4,implies(X3,implies(X2,X4))))),true,is_a_theorem(implies(X4,implies(X3,implies(X2,X4)))),true) = true,
    inference(substitution,[status(thm)],[c410]) ).

cnf(c412,plain,
    ifeq(true,true,is_a_theorem(implies(X4,implies(X3,implies(X2,X4)))),true) = true,
    inference(transitivity,[status(thm)],[c354,c411]) ).

cnf(c413,plain,
    is_a_theorem(implies(X4,implies(X3,implies(X2,X4)))) = true,
    inference(transitivity,[status(thm)],[c328,c412]) ).

cnf(c414,plain,
    is_a_theorem(implies(X2,implies(X4,implies(X3,X2)))) = true,
    inference(substitution,[status(thm)],[c413]) ).

cnf(c415,plain,
    true = is_a_theorem(implies(X2,implies(X4,implies(X3,X2)))),
    inference(symmetry,[status(thm)],[c414]) ).

cnf(c416,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(X3,X2))),true) = ifeq(is_a_theorem(implies(X3,implies(X5,implies(X4,X3)))),true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(X3,X2))),true),
    inference(congruence,[status(thm)],[c415]) ).

cnf(c417,plain,
    ifeq(is_a_theorem(implies(X3,implies(X5,implies(X4,X3)))),true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(X3,X2))),true) = true,
    inference(substitution,[status(thm)],[c92]) ).

cnf(c418,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(X3,X2))),true) = true,
    inference(transitivity,[status(thm)],[c416,c417]) ).

cnf(c419,plain,
    is_a_theorem(implies(implies(implies(X5,implies(X4,X3)),X2),implies(X3,X2))) = true,
    inference(transitivity,[status(thm)],[c326,c418]) ).

cnf(c420,plain,
    is_a_theorem(implies(implies(implies(not(implies(X2,X3)),implies(X2,X3)),implies(X2,X3)),implies(X3,implies(X2,X3)))) = true,
    inference(substitution,[status(thm)],[c419]) ).

cnf(c421,plain,
    true = is_a_theorem(implies(implies(implies(not(implies(X2,X3)),implies(X2,X3)),implies(X2,X3)),implies(X3,implies(X2,X3)))),
    inference(symmetry,[status(thm)],[c420]) ).

cnf(c422,plain,
    ifeq(true,true,is_a_theorem(implies(X3,implies(X2,X3))),true) = ifeq(is_a_theorem(implies(implies(implies(not(implies(X2,X3)),implies(X2,X3)),implies(X2,X3)),implies(X3,implies(X2,X3)))),true,is_a_theorem(implies(X3,implies(X2,X3))),true),
    inference(congruence,[status(thm)],[c421]) ).

cnf(c423,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(implies(X2,X3)),implies(X2,X3)),implies(X2,X3)),implies(X3,implies(X2,X3)))),true,is_a_theorem(implies(X3,implies(X2,X3))),true) = true,
    inference(substitution,[status(thm)],[c47]) ).

cnf(c424,plain,
    ifeq(true,true,is_a_theorem(implies(X3,implies(X2,X3))),true) = true,
    inference(transitivity,[status(thm)],[c422,c423]) ).

cnf(c425,plain,
    is_a_theorem(implies(X3,implies(X2,X3))) = true,
    inference(transitivity,[status(thm)],[c324,c424]) ).

cnf(c426,plain,
    true = is_a_theorem(implies(X3,implies(X2,X3))),
    inference(symmetry,[status(thm)],[c425]) ).

cnf(c427,plain,
    ifeq(true,true,is_a_theorem(X2),true) = ifeq(is_a_theorem(implies(X4,implies(X3,X4))),true,is_a_theorem(X2),true),
    inference(congruence,[status(thm)],[c426]) ).

cnf(c428,plain,
    ifeq(is_a_theorem(implies(implies(X4,implies(X3,X4)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = ifeq(is_a_theorem(implies(implies(X4,implies(X3,X4)),X2)),true,ifeq(is_a_theorem(implies(X4,implies(X3,X4))),true,is_a_theorem(X2),true),true),
    inference(congruence,[status(thm)],[c427]) ).

cnf(c429,plain,
    ifeq(is_a_theorem(implies(implies(X4,implies(X3,X4)),X2)),true,ifeq(is_a_theorem(implies(X4,implies(X3,X4))),true,is_a_theorem(X2),true),true) = true,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c430,plain,
    ifeq(is_a_theorem(implies(implies(X4,implies(X3,X4)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
    inference(transitivity,[status(thm)],[c428,c429]) ).

cnf(c431,plain,
    ifeq(is_a_theorem(implies(implies(X4,implies(X3,X4)),X2)),true,is_a_theorem(X2),true) = true,
    inference(transitivity,[status(thm)],[c322,c430]) ).

cnf(c432,plain,
    ifeq(is_a_theorem(implies(implies(X3,implies(X4,X3)),implies(not(implies(X4,X3)),implies(X3,X2)))),true,is_a_theorem(implies(not(implies(X4,X3)),implies(X3,X2))),true) = true,
    inference(substitution,[status(thm)],[c431]) ).

cnf(c433,plain,
    ifeq(true,true,is_a_theorem(implies(not(implies(X4,X3)),implies(X3,X2))),true) = true,
    inference(transitivity,[status(thm)],[c319,c432]) ).

cnf(c434,plain,
    is_a_theorem(implies(not(implies(X4,X3)),implies(X3,X2))) = true,
    inference(transitivity,[status(thm)],[c6,c433]) ).

cnf(c435,plain,
    is_a_theorem(implies(not(implies(not(implies(X3,X2)),X3)),implies(X3,X2))) = true,
    inference(substitution,[status(thm)],[c434]) ).

cnf(c436,plain,
    true = is_a_theorem(implies(not(implies(not(implies(X3,X2)),X3)),implies(X3,X2))),
    inference(symmetry,[status(thm)],[c435]) ).

cnf(c437,plain,
    ifeq(true,true,is_a_theorem(implies(not(implies(X3,X2)),X3)),true) = ifeq(is_a_theorem(implies(not(implies(not(implies(X3,X2)),X3)),implies(X3,X2))),true,is_a_theorem(implies(not(implies(X3,X2)),X3)),true),
    inference(congruence,[status(thm)],[c436]) ).

cnf(c438,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(not(implies(not(X3),X2)),X3)),true,is_a_theorem(implies(not(X3),X2)),true),true) = ifeq(is_a_theorem(implies(not(implies(not(X3),X2)),X3)),true,is_a_theorem(implies(not(X3),X2)),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c439,plain,
    ifeq(is_a_theorem(implies(not(implies(not(X3),X2)),X3)),true,is_a_theorem(implies(not(X3),X2)),true) = ifeq(true,true,ifeq(is_a_theorem(implies(not(implies(not(X3),X2)),X3)),true,is_a_theorem(implies(not(X3),X2)),true),true),
    inference(symmetry,[status(thm)],[c438]) ).

cnf(c440,plain,
    ifeq(true,true,is_a_theorem(implies(implies(not(implies(not(X3),X2)),X3),implies(not(X3),X2))),true) = is_a_theorem(implies(implies(not(implies(not(X3),X2)),X3),implies(not(X3),X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c441,plain,
    is_a_theorem(implies(implies(not(implies(not(X3),X2)),X3),implies(not(X3),X2))) = ifeq(true,true,is_a_theorem(implies(implies(not(implies(not(X3),X2)),X3),implies(not(X3),X2))),true),
    inference(symmetry,[status(thm)],[c440]) ).

cnf(c442,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X4,implies(not(X4),X3)),implies(not(X2),X2)),X2)),true) = is_a_theorem(implies(implies(implies(X4,implies(not(X4),X3)),implies(not(X2),X2)),X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c443,plain,
    is_a_theorem(implies(implies(implies(X4,implies(not(X4),X3)),implies(not(X2),X2)),X2)) = ifeq(true,true,is_a_theorem(implies(implies(implies(X4,implies(not(X4),X3)),implies(not(X2),X2)),X2)),true),
    inference(symmetry,[status(thm)],[c442]) ).

cnf(c444,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X5,X4),implies(implies(implies(X3,implies(not(X3),X2)),X5),X4))),true) = is_a_theorem(implies(implies(X5,X4),implies(implies(implies(X3,implies(not(X3),X2)),X5),X4))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c445,plain,
    is_a_theorem(implies(implies(X5,X4),implies(implies(implies(X3,implies(not(X3),X2)),X5),X4))) = ifeq(true,true,is_a_theorem(implies(implies(X5,X4),implies(implies(implies(X3,implies(not(X3),X2)),X5),X4))),true),
    inference(symmetry,[status(thm)],[c444]) ).

cnf(c446,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(not(X5),X4)),X3),implies(not(X3),X2))),true) = is_a_theorem(implies(implies(implies(X5,implies(not(X5),X4)),X3),implies(not(X3),X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c447,plain,
    is_a_theorem(implies(implies(implies(X5,implies(not(X5),X4)),X3),implies(not(X3),X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(not(X5),X4)),X3),implies(not(X3),X2))),true),
    inference(symmetry,[status(thm)],[c446]) ).

cnf(c448,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(X5,implies(not(X5),X4))),X3),X2),implies(not(X2),X6))),true) = is_a_theorem(implies(implies(implies(not(implies(X5,implies(not(X5),X4))),X3),X2),implies(not(X2),X6))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c449,plain,
    is_a_theorem(implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(not(X3),X2))) = ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(not(X3),X2))),true),
    inference(symmetry,[status(thm)],[c448]) ).

cnf(c450,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X6,X5),implies(implies(implies(not(implies(X4,implies(not(X4),X3))),X2),X6),X5))),true) = is_a_theorem(implies(implies(X6,X5),implies(implies(implies(not(implies(X4,implies(not(X4),X3))),X2),X6),X5))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c451,plain,
    is_a_theorem(implies(implies(X6,X5),implies(implies(implies(not(implies(X4,implies(not(X4),X3))),X2),X6),X5))) = ifeq(true,true,is_a_theorem(implies(implies(X6,X5),implies(implies(implies(not(implies(X4,implies(not(X4),X3))),X2),X6),X5))),true),
    inference(symmetry,[status(thm)],[c450]) ).

cnf(c452,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(X2,X3))),true) = is_a_theorem(implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(X2,X3))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c453,plain,
    is_a_theorem(implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(X2,X3))) = ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(X2,X3))),true),
    inference(symmetry,[status(thm)],[c452]) ).

cnf(c454,plain,
    ifeq(true,true,is_a_theorem(implies(X5,implies(not(implies(X4,implies(not(X4),X3))),X2))),true) = is_a_theorem(implies(X5,implies(not(implies(X4,implies(not(X4),X3))),X2))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c455,plain,
    is_a_theorem(implies(X5,implies(not(implies(X4,implies(not(X4),X3))),X2))) = ifeq(true,true,is_a_theorem(implies(X5,implies(not(implies(X4,implies(not(X4),X3))),X2))),true),
    inference(symmetry,[status(thm)],[c454]) ).

cnf(c456,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X5,X4),implies(not(implies(X3,implies(not(X3),X2))),X4))),true) = is_a_theorem(implies(implies(X5,X4),implies(not(implies(X3,implies(not(X3),X2))),X4))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c457,plain,
    is_a_theorem(implies(implies(X5,X4),implies(not(implies(X3,implies(not(X3),X2))),X4))) = ifeq(true,true,is_a_theorem(implies(implies(X5,X4),implies(not(implies(X3,implies(not(X3),X2))),X4))),true),
    inference(symmetry,[status(thm)],[c456]) ).

cnf(c458,plain,
    ifeq(true,true,is_a_theorem(implies(not(implies(X4,implies(not(X4),X3))),X2)),true) = is_a_theorem(implies(not(implies(X4,implies(not(X4),X3))),X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c459,plain,
    is_a_theorem(implies(not(implies(X4,implies(not(X4),X3))),X2)) = ifeq(true,true,is_a_theorem(implies(not(implies(X4,implies(not(X4),X3))),X2)),true),
    inference(symmetry,[status(thm)],[c458]) ).

cnf(c460,plain,
    is_a_theorem(implies(X3,implies(not(X3),X2))) = true,
    inference(substitution,[status(thm)],[c64]) ).

cnf(c461,plain,
    true = is_a_theorem(implies(X3,implies(not(X3),X2))),
    inference(symmetry,[status(thm)],[c460]) ).

cnf(c462,plain,
    ifeq(true,true,is_a_theorem(implies(not(implies(X4,implies(not(X4),X3))),X2)),true) = ifeq(is_a_theorem(implies(X4,implies(not(X4),X3))),true,is_a_theorem(implies(not(implies(X4,implies(not(X4),X3))),X2)),true),
    inference(congruence,[status(thm)],[c461]) ).

cnf(c463,plain,
    ifeq(is_a_theorem(implies(X4,implies(not(X4),X3))),true,is_a_theorem(implies(not(implies(X4,implies(not(X4),X3))),X2)),true) = true,
    inference(substitution,[status(thm)],[c377]) ).

cnf(c464,plain,
    ifeq(true,true,is_a_theorem(implies(not(implies(X4,implies(not(X4),X3))),X2)),true) = true,
    inference(transitivity,[status(thm)],[c462,c463]) ).

cnf(c465,plain,
    is_a_theorem(implies(not(implies(X4,implies(not(X4),X3))),X2)) = true,
    inference(transitivity,[status(thm)],[c459,c464]) ).

cnf(c466,plain,
    is_a_theorem(implies(not(implies(X3,implies(not(X3),X2))),X4)) = true,
    inference(substitution,[status(thm)],[c465]) ).

cnf(c467,plain,
    true = is_a_theorem(implies(not(implies(X3,implies(not(X3),X2))),X4)),
    inference(symmetry,[status(thm)],[c466]) ).

cnf(c468,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X5,X4),implies(not(implies(X3,implies(not(X3),X2))),X4))),true) = ifeq(is_a_theorem(implies(not(implies(X3,implies(not(X3),X2))),X5)),true,is_a_theorem(implies(implies(X5,X4),implies(not(implies(X3,implies(not(X3),X2))),X4))),true),
    inference(congruence,[status(thm)],[c467]) ).

cnf(c469,plain,
    ifeq(is_a_theorem(implies(not(implies(X3,implies(not(X3),X2))),X5)),true,is_a_theorem(implies(implies(X5,X4),implies(not(implies(X3,implies(not(X3),X2))),X4))),true) = true,
    inference(substitution,[status(thm)],[c92]) ).

cnf(c470,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X5,X4),implies(not(implies(X3,implies(not(X3),X2))),X4))),true) = true,
    inference(transitivity,[status(thm)],[c468,c469]) ).

cnf(c471,plain,
    is_a_theorem(implies(implies(X5,X4),implies(not(implies(X3,implies(not(X3),X2))),X4))) = true,
    inference(transitivity,[status(thm)],[c457,c470]) ).

cnf(c472,plain,
    is_a_theorem(implies(implies(not(X5),X2),implies(not(implies(X4,implies(not(X4),X3))),X2))) = true,
    inference(substitution,[status(thm)],[c471]) ).

cnf(c473,plain,
    true = is_a_theorem(implies(implies(not(X5),X2),implies(not(implies(X4,implies(not(X4),X3))),X2))),
    inference(symmetry,[status(thm)],[c472]) ).

cnf(c474,plain,
    ifeq(true,true,is_a_theorem(implies(X5,implies(not(implies(X4,implies(not(X4),X3))),X2))),true) = ifeq(is_a_theorem(implies(implies(not(X5),X2),implies(not(implies(X4,implies(not(X4),X3))),X2))),true,is_a_theorem(implies(X5,implies(not(implies(X4,implies(not(X4),X3))),X2))),true),
    inference(congruence,[status(thm)],[c473]) ).

cnf(c475,plain,
    ifeq(is_a_theorem(implies(implies(not(X5),X2),implies(not(implies(X4,implies(not(X4),X3))),X2))),true,is_a_theorem(implies(X5,implies(not(implies(X4,implies(not(X4),X3))),X2))),true) = true,
    inference(substitution,[status(thm)],[c79]) ).

cnf(c476,plain,
    ifeq(true,true,is_a_theorem(implies(X5,implies(not(implies(X4,implies(not(X4),X3))),X2))),true) = true,
    inference(transitivity,[status(thm)],[c474,c475]) ).

cnf(c477,plain,
    is_a_theorem(implies(X5,implies(not(implies(X4,implies(not(X4),X3))),X2))) = true,
    inference(transitivity,[status(thm)],[c455,c476]) ).

cnf(c478,plain,
    is_a_theorem(implies(X2,implies(not(implies(X5,implies(not(X5),X4))),X3))) = true,
    inference(substitution,[status(thm)],[c477]) ).

cnf(c479,plain,
    true = is_a_theorem(implies(X2,implies(not(implies(X5,implies(not(X5),X4))),X3))),
    inference(symmetry,[status(thm)],[c478]) ).

cnf(c480,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(X2,X3))),true) = ifeq(is_a_theorem(implies(X2,implies(not(implies(X6,implies(not(X6),X5))),X4))),true,is_a_theorem(implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(X2,X3))),true),
    inference(congruence,[status(thm)],[c479]) ).

cnf(c481,plain,
    ifeq(is_a_theorem(implies(X2,implies(not(implies(X6,implies(not(X6),X5))),X4))),true,is_a_theorem(implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(X2,X3))),true) = true,
    inference(substitution,[status(thm)],[c92]) ).

cnf(c482,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(X2,X3))),true) = true,
    inference(transitivity,[status(thm)],[c480,c481]) ).

cnf(c483,plain,
    is_a_theorem(implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(X2,X3))) = true,
    inference(transitivity,[status(thm)],[c453,c482]) ).

cnf(c484,plain,
    is_a_theorem(implies(implies(implies(not(implies(X4,implies(not(X4),X3))),X2),X5),implies(not(X5),X5))) = true,
    inference(substitution,[status(thm)],[c483]) ).

cnf(c485,plain,
    true = is_a_theorem(implies(implies(implies(not(implies(X4,implies(not(X4),X3))),X2),X5),implies(not(X5),X5))),
    inference(symmetry,[status(thm)],[c484]) ).

cnf(c486,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X6,X5),implies(implies(implies(not(implies(X4,implies(not(X4),X3))),X2),X6),X5))),true) = ifeq(is_a_theorem(implies(implies(implies(not(implies(X4,implies(not(X4),X3))),X2),X6),implies(not(X6),X6))),true,is_a_theorem(implies(implies(X6,X5),implies(implies(implies(not(implies(X4,implies(not(X4),X3))),X2),X6),X5))),true),
    inference(congruence,[status(thm)],[c485]) ).

cnf(c487,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(implies(X4,implies(not(X4),X3))),X2),X6),implies(not(X6),X6))),true,is_a_theorem(implies(implies(X6,X5),implies(implies(implies(not(implies(X4,implies(not(X4),X3))),X2),X6),X5))),true) = true,
    inference(substitution,[status(thm)],[c213]) ).

cnf(c488,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X6,X5),implies(implies(implies(not(implies(X4,implies(not(X4),X3))),X2),X6),X5))),true) = true,
    inference(transitivity,[status(thm)],[c486,c487]) ).

cnf(c489,plain,
    is_a_theorem(implies(implies(X6,X5),implies(implies(implies(not(implies(X4,implies(not(X4),X3))),X2),X6),X5))) = true,
    inference(transitivity,[status(thm)],[c451,c488]) ).

cnf(c490,plain,
    is_a_theorem(implies(implies(X3,implies(not(X3),X2)),implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(not(X3),X2)))) = true,
    inference(substitution,[status(thm)],[c489]) ).

cnf(c491,plain,
    true = is_a_theorem(implies(implies(X3,implies(not(X3),X2)),implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(not(X3),X2)))),
    inference(symmetry,[status(thm)],[c490]) ).

cnf(c492,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(not(X3),X2))),true) = ifeq(is_a_theorem(implies(implies(X3,implies(not(X3),X2)),implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(not(X3),X2)))),true,is_a_theorem(implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(not(X3),X2))),true),
    inference(congruence,[status(thm)],[c491]) ).

cnf(c493,plain,
    ifeq(is_a_theorem(implies(implies(X3,implies(not(X3),X2)),implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(not(X3),X2)))),true,is_a_theorem(implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(not(X3),X2))),true) = true,
    inference(substitution,[status(thm)],[c71]) ).

cnf(c494,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(not(X3),X2))),true) = true,
    inference(transitivity,[status(thm)],[c492,c493]) ).

cnf(c495,plain,
    is_a_theorem(implies(implies(implies(not(implies(X6,implies(not(X6),X5))),X4),X3),implies(not(X3),X2))) = true,
    inference(transitivity,[status(thm)],[c449,c494]) ).

cnf(c496,plain,
    is_a_theorem(implies(implies(implies(not(implies(X5,implies(not(X5),X4))),implies(X5,implies(not(X5),X4))),X3),implies(not(X3),X2))) = true,
    inference(substitution,[status(thm)],[c495]) ).

cnf(c497,plain,
    true = is_a_theorem(implies(implies(implies(not(implies(X5,implies(not(X5),X4))),implies(X5,implies(not(X5),X4))),X3),implies(not(X3),X2))),
    inference(symmetry,[status(thm)],[c496]) ).

cnf(c498,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(not(X5),X4)),X3),implies(not(X3),X2))),true) = ifeq(is_a_theorem(implies(implies(implies(not(implies(X5,implies(not(X5),X4))),implies(X5,implies(not(X5),X4))),X3),implies(not(X3),X2))),true,is_a_theorem(implies(implies(implies(X5,implies(not(X5),X4)),X3),implies(not(X3),X2))),true),
    inference(congruence,[status(thm)],[c497]) ).

cnf(c499,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(implies(X5,implies(not(X5),X4))),implies(X5,implies(not(X5),X4))),X3),implies(not(X3),X2))),true,is_a_theorem(implies(implies(implies(X5,implies(not(X5),X4)),X3),implies(not(X3),X2))),true) = true,
    inference(substitution,[status(thm)],[c192]) ).

cnf(c500,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X5,implies(not(X5),X4)),X3),implies(not(X3),X2))),true) = true,
    inference(transitivity,[status(thm)],[c498,c499]) ).

cnf(c501,plain,
    is_a_theorem(implies(implies(implies(X5,implies(not(X5),X4)),X3),implies(not(X3),X2))) = true,
    inference(transitivity,[status(thm)],[c447,c500]) ).

cnf(c502,plain,
    is_a_theorem(implies(implies(implies(X3,implies(not(X3),X2)),X4),implies(not(X4),X4))) = true,
    inference(substitution,[status(thm)],[c501]) ).

cnf(c503,plain,
    true = is_a_theorem(implies(implies(implies(X3,implies(not(X3),X2)),X4),implies(not(X4),X4))),
    inference(symmetry,[status(thm)],[c502]) ).

cnf(c504,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X5,X4),implies(implies(implies(X3,implies(not(X3),X2)),X5),X4))),true) = ifeq(is_a_theorem(implies(implies(implies(X3,implies(not(X3),X2)),X5),implies(not(X5),X5))),true,is_a_theorem(implies(implies(X5,X4),implies(implies(implies(X3,implies(not(X3),X2)),X5),X4))),true),
    inference(congruence,[status(thm)],[c503]) ).

cnf(c505,plain,
    ifeq(is_a_theorem(implies(implies(implies(X3,implies(not(X3),X2)),X5),implies(not(X5),X5))),true,is_a_theorem(implies(implies(X5,X4),implies(implies(implies(X3,implies(not(X3),X2)),X5),X4))),true) = true,
    inference(substitution,[status(thm)],[c213]) ).

cnf(c506,plain,
    ifeq(true,true,is_a_theorem(implies(implies(X5,X4),implies(implies(implies(X3,implies(not(X3),X2)),X5),X4))),true) = true,
    inference(transitivity,[status(thm)],[c504,c505]) ).

cnf(c507,plain,
    is_a_theorem(implies(implies(X5,X4),implies(implies(implies(X3,implies(not(X3),X2)),X5),X4))) = true,
    inference(transitivity,[status(thm)],[c445,c506]) ).

cnf(c508,plain,
    is_a_theorem(implies(implies(implies(not(X2),X2),X2),implies(implies(implies(X4,implies(not(X4),X3)),implies(not(X2),X2)),X2))) = true,
    inference(substitution,[status(thm)],[c507]) ).

cnf(c509,plain,
    true = is_a_theorem(implies(implies(implies(not(X2),X2),X2),implies(implies(implies(X4,implies(not(X4),X3)),implies(not(X2),X2)),X2))),
    inference(symmetry,[status(thm)],[c508]) ).

cnf(c510,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X4,implies(not(X4),X3)),implies(not(X2),X2)),X2)),true) = ifeq(is_a_theorem(implies(implies(implies(not(X2),X2),X2),implies(implies(implies(X4,implies(not(X4),X3)),implies(not(X2),X2)),X2))),true,is_a_theorem(implies(implies(implies(X4,implies(not(X4),X3)),implies(not(X2),X2)),X2)),true),
    inference(congruence,[status(thm)],[c509]) ).

cnf(c511,plain,
    ifeq(is_a_theorem(implies(implies(implies(not(X2),X2),X2),implies(implies(implies(X4,implies(not(X4),X3)),implies(not(X2),X2)),X2))),true,is_a_theorem(implies(implies(implies(X4,implies(not(X4),X3)),implies(not(X2),X2)),X2)),true) = true,
    inference(substitution,[status(thm)],[c47]) ).

cnf(c512,plain,
    ifeq(true,true,is_a_theorem(implies(implies(implies(X4,implies(not(X4),X3)),implies(not(X2),X2)),X2)),true) = true,
    inference(transitivity,[status(thm)],[c510,c511]) ).

cnf(c513,plain,
    is_a_theorem(implies(implies(implies(X4,implies(not(X4),X3)),implies(not(X2),X2)),X2)) = true,
    inference(transitivity,[status(thm)],[c443,c512]) ).

cnf(c514,plain,
    is_a_theorem(implies(implies(implies(X3,implies(not(X3),X2)),implies(not(implies(not(X3),X2)),implies(not(X3),X2))),implies(not(X3),X2))) = true,
    inference(substitution,[status(thm)],[c513]) ).

cnf(c515,plain,
    true = is_a_theorem(implies(implies(implies(X3,implies(not(X3),X2)),implies(not(implies(not(X3),X2)),implies(not(X3),X2))),implies(not(X3),X2))),
    inference(symmetry,[status(thm)],[c514]) ).

cnf(c516,plain,
    ifeq(true,true,is_a_theorem(implies(implies(not(implies(not(X3),X2)),X3),implies(not(X3),X2))),true) = ifeq(is_a_theorem(implies(implies(implies(X3,implies(not(X3),X2)),implies(not(implies(not(X3),X2)),implies(not(X3),X2))),implies(not(X3),X2))),true,is_a_theorem(implies(implies(not(implies(not(X3),X2)),X3),implies(not(X3),X2))),true),
    inference(congruence,[status(thm)],[c515]) ).

cnf(c517,plain,
    ifeq(is_a_theorem(implies(implies(implies(X3,implies(not(X3),X2)),implies(not(implies(not(X3),X2)),implies(not(X3),X2))),implies(not(X3),X2))),true,is_a_theorem(implies(implies(not(implies(not(X3),X2)),X3),implies(not(X3),X2))),true) = true,
    inference(substitution,[status(thm)],[c113]) ).

cnf(c518,plain,
    ifeq(true,true,is_a_theorem(implies(implies(not(implies(not(X3),X2)),X3),implies(not(X3),X2))),true) = true,
    inference(transitivity,[status(thm)],[c516,c517]) ).

cnf(c519,plain,
    is_a_theorem(implies(implies(not(implies(not(X3),X2)),X3),implies(not(X3),X2))) = true,
    inference(transitivity,[status(thm)],[c441,c518]) ).

cnf(c520,plain,
    true = is_a_theorem(implies(implies(not(implies(not(X3),X2)),X3),implies(not(X3),X2))),
    inference(symmetry,[status(thm)],[c519]) ).

cnf(c521,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(not(implies(not(X3),X2)),X3)),true,is_a_theorem(implies(not(X3),X2)),true),true) = ifeq(is_a_theorem(implies(implies(not(implies(not(X3),X2)),X3),implies(not(X3),X2))),true,ifeq(is_a_theorem(implies(not(implies(not(X3),X2)),X3)),true,is_a_theorem(implies(not(X3),X2)),true),true),
    inference(congruence,[status(thm)],[c520]) ).

cnf(c522,plain,
    ifeq(is_a_theorem(implies(implies(not(implies(not(X3),X2)),X3),implies(not(X3),X2))),true,ifeq(is_a_theorem(implies(not(implies(not(X3),X2)),X3)),true,is_a_theorem(implies(not(X3),X2)),true),true) = true,
    inference(substitution,[status(thm)],[c44]) ).

cnf(c523,plain,
    ifeq(true,true,ifeq(is_a_theorem(implies(not(implies(not(X3),X2)),X3)),true,is_a_theorem(implies(not(X3),X2)),true),true) = true,
    inference(transitivity,[status(thm)],[c521,c522]) ).

cnf(c524,plain,
    ifeq(is_a_theorem(implies(not(implies(not(X3),X2)),X3)),true,is_a_theorem(implies(not(X3),X2)),true) = true,
    inference(transitivity,[status(thm)],[c439,c523]) ).

cnf(c525,plain,
    ifeq(is_a_theorem(implies(not(implies(not(implies(X3,X2)),X3)),implies(X3,X2))),true,is_a_theorem(implies(not(implies(X3,X2)),X3)),true) = true,
    inference(substitution,[status(thm)],[c524]) ).

cnf(c526,plain,
    ifeq(true,true,is_a_theorem(implies(not(implies(X3,X2)),X3)),true) = true,
    inference(transitivity,[status(thm)],[c437,c525]) ).

cnf(c527,plain,
    is_a_theorem(implies(not(implies(X3,X2)),X3)) = true,
    inference(transitivity,[status(thm)],[c4,c526]) ).

cnf(c528,plain,
    is_a_theorem(implies(not(implies(x,y)),x)) = true,
    inference(substitution,[status(thm)],[c527]) ).

cnf(c529,plain,
    $false,
    inference(resolution,[status(thm)],[c1,c528]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04  % Problem  : LCL400-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06  % Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42  % Computer : n009.cluster.edu
% 0.15/0.42  % Model    : x86_64 x86_64
% 0.15/0.42  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42  % Memory   : 8046.5625MB
% 0.15/0.42  % OS       : Linux 6.8.0-71-generic
% 0.15/0.42  % CPULimit : 300
% 0.15/0.42  % WCLimit  : 300
% 0.15/0.42  % DateTime : Sun Sep 27 15:40:14 UTC 2026
% 0.15/0.42  % CPUTime  : 
% 0.15/0.42  Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 81.82/10.90  Command-line arguments: --no-flatten-goal
% 81.82/10.90  
% 81.82/10.90  % SZS status Unsatisfiable
% 81.82/10.90  
% 82.65/10.94  % SZS output start CNFRefutation
% See solution above
% 86.57/11.44  
% 86.57/11.44  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------