Twee---2.7.UNS-CRf.s

%------------------------------------------------------------------------------
% File     : Twee---2.7
% Problem  : LCL416-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n010.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 11:49:48 AM UTC 2026

% Result   : Unsatisfiable 156.87s 20.29s
% Output   : CNFRefutation 160.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   95
%            Number of leaves      :    4
% Syntax   : Number of clauses     :  239 ( 239 unt;   0 nHn;   3 RR)
%            Number of literals    :  239 ( 238 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   16 (   3 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-4 aty)
%            Number of variables   : 1190 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
    is_a_theorem(equivalent(a,a)) != true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_reflexivity) ).

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(equivalent(X,X)),true) = is_a_theorem(equivalent(X,X)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c4,plain,
    is_a_theorem(equivalent(X,X)) = ifeq(true,true,is_a_theorem(equivalent(X,X)),true),
    inference(symmetry,[status(thm)],[c3]) ).

cnf(c5,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,X3),equivalent(X,X3)),X2),X2)),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,X3),equivalent(X,X3)),X2),X2)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c6,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X)) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X)),true),
    inference(symmetry,[status(thm)],[c5]) ).

cnf(c7,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(X3,equivalent(equivalent(equivalent(equivalent(X2,X),equivalent(X2,X)),equivalent(equivalent(equivalent(equivalent(X7,X6),equivalent(X7,X6)),X5),equivalent(X4,X5))),X4)),X3)),true) = is_a_theorem(equivalent(equivalent(X3,equivalent(equivalent(equivalent(equivalent(X2,X),equivalent(X2,X)),equivalent(equivalent(equivalent(equivalent(X7,X6),equivalent(X7,X6)),X5),equivalent(X4,X5))),X4)),X3)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c8,plain,
    is_a_theorem(equivalent(equivalent(X7,equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),X)),X7)) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X7,equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),X)),X7)),true),
    inference(symmetry,[status(thm)],[c7]) ).

cnf(c9,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(X,X2)),X)),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(X,X2)),X)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c10,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(X,X2)),X)) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(X,X2)),X)),true),
    inference(symmetry,[status(thm)],[c9]) ).

cnf(c11,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2)),X)),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2)),X)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c12,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2)),X)) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2)),X)),true),
    inference(symmetry,[status(thm)],[c11]) ).

cnf(c13,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(X2,X),equivalent(X2,X))),true) = is_a_theorem(equivalent(equivalent(X2,X),equivalent(X2,X))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c14,plain,
    is_a_theorem(equivalent(equivalent(X2,X),equivalent(X2,X))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X2,X),equivalent(X2,X))),true),
    inference(symmetry,[status(thm)],[c13]) ).

cnf(c15,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),true) = is_a_theorem(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c16,plain,
    is_a_theorem(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),true),
    inference(symmetry,[status(thm)],[c15]) ).

cnf(c17,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),X4)),true) = is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),X4)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c18,plain,
    is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),X4)) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),X4)),true),
    inference(symmetry,[status(thm)],[c17]) ).

cnf(c19,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),equivalent(X4,equivalent(equivalent(equivalent(X4,X3),equivalent(X2,X3)),X2))),X),equivalent(X8,X)),X8)),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),equivalent(X4,equivalent(equivalent(equivalent(X4,X3),equivalent(X2,X3)),X2))),X),equivalent(X8,X)),X8)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c20,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X8,equivalent(equivalent(equivalent(X8,X7),equivalent(X6,X7)),X6)),equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),X2),equivalent(X,X2)),X)) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X8,equivalent(equivalent(equivalent(X8,X7),equivalent(X6,X7)),X6)),equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),X2),equivalent(X,X2)),X)),true),
    inference(symmetry,[status(thm)],[c19]) ).

cnf(c21,plain,
    ifeq(true,true,is_a_theorem(equivalent(X6,equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),X2),equivalent(X,X2)),X))),true) = is_a_theorem(equivalent(X6,equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),X2),equivalent(X,X2)),X))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c22,plain,
    is_a_theorem(equivalent(X6,equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),X2),equivalent(X,X2)),X))) = ifeq(true,true,is_a_theorem(equivalent(X6,equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),X2),equivalent(X,X2)),X))),true),
    inference(symmetry,[status(thm)],[c21]) ).

cnf(c23,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),X),equivalent(X2,X))),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),X),equivalent(X2,X))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c24,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),X),equivalent(X2,X))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),X),equivalent(X2,X))),true),
    inference(symmetry,[status(thm)],[c23]) ).

cnf(c25,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X)),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c26,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X)) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X)),true),
    inference(symmetry,[status(thm)],[c25]) ).

cnf(c27,axiom,
    is_a_theorem(equivalent(A2,equivalent(equivalent(equivalent(A2,B2),equivalent(C2,B2)),C2))) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xcb) ).

cnf(c28,plain,
    is_a_theorem(equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))) = true,
    inference(substitution,[status(thm)],[c27]) ).

cnf(c29,plain,
    true = is_a_theorem(equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),
    inference(symmetry,[status(thm)],[c28]) ).

cnf(c30,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X)),true) = ifeq(is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X)),true),
    inference(congruence,[status(thm)],[c29]) ).

cnf(c31,plain,
    ifeq(true,true,ifeq(is_a_theorem(X3),true,is_a_theorem(equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),true),true) = ifeq(is_a_theorem(X3),true,is_a_theorem(equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c32,plain,
    ifeq(is_a_theorem(X3),true,is_a_theorem(equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),true) = ifeq(true,true,ifeq(is_a_theorem(X3),true,is_a_theorem(equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),true),true),
    inference(symmetry,[status(thm)],[c31]) ).

cnf(c33,plain,
    is_a_theorem(equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))) = true,
    inference(substitution,[status(thm)],[c27]) ).

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

cnf(c35,plain,
    ifeq(true,true,ifeq(is_a_theorem(X3),true,is_a_theorem(equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),true),true) = ifeq(is_a_theorem(equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),true,ifeq(is_a_theorem(X3),true,is_a_theorem(equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),true),true),
    inference(congruence,[status(thm)],[c34]) ).

cnf(c36,axiom,
    ifeq(is_a_theorem(equivalent(A2,B2)),true,ifeq(is_a_theorem(A2),true,is_a_theorem(B2),true),true) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).

cnf(c37,plain,
    ifeq(is_a_theorem(equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),true,ifeq(is_a_theorem(X3),true,is_a_theorem(equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),true),true) = true,
    inference(substitution,[status(thm)],[c36]) ).

cnf(c38,plain,
    ifeq(true,true,ifeq(is_a_theorem(X3),true,is_a_theorem(equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),true),true) = true,
    inference(transitivity,[status(thm)],[c35,c37]) ).

cnf(c39,plain,
    ifeq(is_a_theorem(X3),true,is_a_theorem(equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),true) = true,
    inference(transitivity,[status(thm)],[c32,c38]) ).

cnf(c40,plain,
    ifeq(is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X)),true) = true,
    inference(substitution,[status(thm)],[c39]) ).

cnf(c41,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X)),true) = true,
    inference(transitivity,[status(thm)],[c30,c40]) ).

cnf(c42,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X)) = true,
    inference(transitivity,[status(thm)],[c26,c41]) ).

cnf(c43,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),X),equivalent(X2,X)),X2)),equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),X),equivalent(X2,X)))) = true,
    inference(substitution,[status(thm)],[c42]) ).

cnf(c44,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),X),equivalent(X2,X)),X2)),equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),X),equivalent(X2,X)))),
    inference(symmetry,[status(thm)],[c43]) ).

cnf(c45,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),X),equivalent(X2,X))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),X),equivalent(X2,X)),X2)),equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),X),equivalent(X2,X)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),X),equivalent(X2,X))),true),
    inference(congruence,[status(thm)],[c44]) ).

cnf(c46,plain,
    ifeq(true,true,is_a_theorem(X),true) = is_a_theorem(X),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c47,plain,
    is_a_theorem(X) = ifeq(true,true,is_a_theorem(X),true),
    inference(symmetry,[status(thm)],[c46]) ).

cnf(c48,plain,
    ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(equivalent(X4,X3),equivalent(X2,X3)),X2)),X)),true,is_a_theorem(X),true) = ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(equivalent(X4,X3),equivalent(X2,X3)),X2)),X)),true,ifeq(true,true,is_a_theorem(X),true),true),
    inference(congruence,[status(thm)],[c47]) ).

cnf(c49,plain,
    is_a_theorem(equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))) = true,
    inference(substitution,[status(thm)],[c27]) ).

cnf(c50,plain,
    true = is_a_theorem(equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),
    inference(symmetry,[status(thm)],[c49]) ).

cnf(c51,plain,
    ifeq(true,true,is_a_theorem(X),true) = ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(equivalent(X4,X3),equivalent(X2,X3)),X2))),true,is_a_theorem(X),true),
    inference(congruence,[status(thm)],[c50]) ).

cnf(c52,plain,
    ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(equivalent(X4,X3),equivalent(X2,X3)),X2)),X)),true,ifeq(true,true,is_a_theorem(X),true),true) = ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(equivalent(X4,X3),equivalent(X2,X3)),X2)),X)),true,ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(equivalent(X4,X3),equivalent(X2,X3)),X2))),true,is_a_theorem(X),true),true),
    inference(congruence,[status(thm)],[c51]) ).

cnf(c53,plain,
    ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(equivalent(X4,X3),equivalent(X2,X3)),X2)),X)),true,ifeq(is_a_theorem(equivalent(X4,equivalent(equivalent(equivalent(X4,X3),equivalent(X2,X3)),X2))),true,is_a_theorem(X),true),true) = true,
    inference(substitution,[status(thm)],[c36]) ).

cnf(c54,plain,
    ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(equivalent(X4,X3),equivalent(X2,X3)),X2)),X)),true,ifeq(true,true,is_a_theorem(X),true),true) = true,
    inference(transitivity,[status(thm)],[c52,c53]) ).

cnf(c55,plain,
    ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(equivalent(equivalent(X4,X3),equivalent(X2,X3)),X2)),X)),true,is_a_theorem(X),true) = true,
    inference(transitivity,[status(thm)],[c48,c54]) ).

cnf(c56,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),X),equivalent(X2,X)),X2)),equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),X),equivalent(X2,X)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),X),equivalent(X2,X))),true) = true,
    inference(substitution,[status(thm)],[c55]) ).

cnf(c57,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),X),equivalent(X2,X))),true) = true,
    inference(transitivity,[status(thm)],[c45,c56]) ).

cnf(c58,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),X),equivalent(X2,X))) = true,
    inference(transitivity,[status(thm)],[c24,c57]) ).

cnf(c59,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),X2),equivalent(X,X2)),X)),equivalent(X6,equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),X2),equivalent(X,X2)),X)))) = true,
    inference(substitution,[status(thm)],[c58]) ).

cnf(c60,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),X2),equivalent(X,X2)),X)),equivalent(X6,equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),X2),equivalent(X,X2)),X)))),
    inference(symmetry,[status(thm)],[c59]) ).

cnf(c61,plain,
    ifeq(true,true,is_a_theorem(equivalent(X6,equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),X2),equivalent(X,X2)),X))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),X2),equivalent(X,X2)),X)),equivalent(X6,equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),X2),equivalent(X,X2)),X)))),true,is_a_theorem(equivalent(X6,equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),X2),equivalent(X,X2)),X))),true),
    inference(congruence,[status(thm)],[c60]) ).

cnf(c62,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),X2),equivalent(X,X2)),X)),equivalent(X6,equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),X2),equivalent(X,X2)),X)))),true,is_a_theorem(equivalent(X6,equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),X2),equivalent(X,X2)),X))),true) = true,
    inference(substitution,[status(thm)],[c55]) ).

cnf(c63,plain,
    ifeq(true,true,is_a_theorem(equivalent(X6,equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),X2),equivalent(X,X2)),X))),true) = true,
    inference(transitivity,[status(thm)],[c61,c62]) ).

cnf(c64,plain,
    is_a_theorem(equivalent(X6,equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X6),X2),equivalent(X,X2)),X))) = true,
    inference(transitivity,[status(thm)],[c22,c63]) ).

cnf(c65,plain,
    is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),equivalent(equivalent(equivalent(equivalent(equivalent(X8,equivalent(equivalent(equivalent(X8,X7),equivalent(X6,X7)),X6)),equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),X2),equivalent(X,X2)),X))) = true,
    inference(substitution,[status(thm)],[c64]) ).

cnf(c66,plain,
    true = is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),equivalent(equivalent(equivalent(equivalent(equivalent(X8,equivalent(equivalent(equivalent(X8,X7),equivalent(X6,X7)),X6)),equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),X2),equivalent(X,X2)),X))),
    inference(symmetry,[status(thm)],[c65]) ).

cnf(c67,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X8,equivalent(equivalent(equivalent(X8,X7),equivalent(X6,X7)),X6)),equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),X2),equivalent(X,X2)),X)),true) = ifeq(is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),equivalent(equivalent(equivalent(equivalent(equivalent(X8,equivalent(equivalent(equivalent(X8,X7),equivalent(X6,X7)),X6)),equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),X2),equivalent(X,X2)),X))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X8,equivalent(equivalent(equivalent(X8,X7),equivalent(X6,X7)),X6)),equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),X2),equivalent(X,X2)),X)),true),
    inference(congruence,[status(thm)],[c66]) ).

cnf(c68,plain,
    ifeq(is_a_theorem(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),equivalent(equivalent(equivalent(equivalent(equivalent(X8,equivalent(equivalent(equivalent(X8,X7),equivalent(X6,X7)),X6)),equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),X2),equivalent(X,X2)),X))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X8,equivalent(equivalent(equivalent(X8,X7),equivalent(X6,X7)),X6)),equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),X2),equivalent(X,X2)),X)),true) = true,
    inference(substitution,[status(thm)],[c55]) ).

cnf(c69,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X8,equivalent(equivalent(equivalent(X8,X7),equivalent(X6,X7)),X6)),equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),X2),equivalent(X,X2)),X)),true) = true,
    inference(transitivity,[status(thm)],[c67,c68]) ).

cnf(c70,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X8,equivalent(equivalent(equivalent(X8,X7),equivalent(X6,X7)),X6)),equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),X2),equivalent(X,X2)),X)) = true,
    inference(transitivity,[status(thm)],[c20,c69]) ).

cnf(c71,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X)),equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X))),equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),equivalent(X6,equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)))),X6)) = true,
    inference(substitution,[status(thm)],[c70]) ).

cnf(c72,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X)),equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X))),equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),equivalent(X6,equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)))),X6)),
    inference(symmetry,[status(thm)],[c71]) ).

cnf(c73,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(X6,equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),X6)),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X)),equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X))),equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),equivalent(X6,equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)))),X6)),true,is_a_theorem(equivalent(equivalent(X6,equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),X6)),true),
    inference(congruence,[status(thm)],[c72]) ).

cnf(c74,plain,
    ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c75,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X)),true,is_a_theorem(equivalent(X2,X)),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),true),
    inference(symmetry,[status(thm)],[c74]) ).

cnf(c76,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X))),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c77,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X))),true),
    inference(symmetry,[status(thm)],[c76]) ).

cnf(c78,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(X,X2)),X)),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(X,X2)),X)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c79,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(X,X2)),X)) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(X,X2)),X)),true),
    inference(symmetry,[status(thm)],[c78]) ).

cnf(c80,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X)),
    inference(symmetry,[status(thm)],[c42]) ).

cnf(c81,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(X,X2)),X)),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3)),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(X,X2)),X)),true),
    inference(congruence,[status(thm)],[c80]) ).

cnf(c82,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3)),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(X,X2)),X)),true) = true,
    inference(substitution,[status(thm)],[c39]) ).

cnf(c83,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(X,X2)),X)),true) = true,
    inference(transitivity,[status(thm)],[c81,c82]) ).

cnf(c84,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(X,X2)),X)) = true,
    inference(transitivity,[status(thm)],[c79,c83]) ).

cnf(c85,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X)),X2)),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X)))) = true,
    inference(substitution,[status(thm)],[c84]) ).

cnf(c86,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X)),X2)),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X)))),
    inference(symmetry,[status(thm)],[c85]) ).

cnf(c87,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X)),X2)),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X))),true),
    inference(congruence,[status(thm)],[c86]) ).

cnf(c88,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X)),X2)),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X))),true) = true,
    inference(substitution,[status(thm)],[c55]) ).

cnf(c89,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X))),true) = true,
    inference(transitivity,[status(thm)],[c87,c88]) ).

cnf(c90,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X))) = true,
    inference(transitivity,[status(thm)],[c77,c89]) ).

cnf(c91,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X))),
    inference(symmetry,[status(thm)],[c90]) ).

cnf(c92,plain,
    ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),true),
    inference(congruence,[status(thm)],[c91]) ).

cnf(c93,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X),equivalent(X2,X))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),true) = true,
    inference(substitution,[status(thm)],[c36]) ).

cnf(c94,plain,
    ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),true) = true,
    inference(transitivity,[status(thm)],[c92,c93]) ).

cnf(c95,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X7,equivalent(equivalent(equivalent(X7,X6),equivalent(X5,X6)),X5)),X4),equivalent(X3,X4)),X3),X2),X)),true,is_a_theorem(equivalent(X2,X)),true) = true,
    inference(transitivity,[status(thm)],[c75,c94]) ).

cnf(c96,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X)),equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X))),equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),equivalent(X6,equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)))),X6)),true,is_a_theorem(equivalent(equivalent(X6,equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3))),X6)),true) = true,
    inference(substitution,[status(thm)],[c95]) ).

cnf(c97,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),X4)),true) = true,
    inference(transitivity,[status(thm)],[c73,c96]) ).

cnf(c98,plain,
    is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),X4)) = true,
    inference(transitivity,[status(thm)],[c18,c97]) ).

cnf(c99,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)))) = true,
    inference(substitution,[status(thm)],[c98]) ).

cnf(c100,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)))),
    inference(symmetry,[status(thm)],[c99]) ).

cnf(c101,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)))),true,is_a_theorem(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),true),
    inference(congruence,[status(thm)],[c100]) ).

cnf(c102,plain,
    ifeq(true,true,is_a_theorem(X),true) = is_a_theorem(X),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c103,plain,
    is_a_theorem(X) = ifeq(true,true,is_a_theorem(X),true),
    inference(symmetry,[status(thm)],[c102]) ).

cnf(c104,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),X2),equivalent(X3,X2)),X)),true,is_a_theorem(X),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),X2),equivalent(X3,X2)),X)),true,ifeq(true,true,is_a_theorem(X),true),true),
    inference(congruence,[status(thm)],[c103]) ).

cnf(c105,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),X),equivalent(X2,X))),
    inference(symmetry,[status(thm)],[c58]) ).

cnf(c106,plain,
    ifeq(true,true,is_a_theorem(X),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),X2),equivalent(X3,X2))),true,is_a_theorem(X),true),
    inference(congruence,[status(thm)],[c105]) ).

cnf(c107,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),X2),equivalent(X3,X2)),X)),true,ifeq(true,true,is_a_theorem(X),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),X2),equivalent(X3,X2)),X)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),X2),equivalent(X3,X2))),true,is_a_theorem(X),true),true),
    inference(congruence,[status(thm)],[c106]) ).

cnf(c108,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),X2),equivalent(X3,X2)),X)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),X2),equivalent(X3,X2))),true,is_a_theorem(X),true),true) = true,
    inference(substitution,[status(thm)],[c36]) ).

cnf(c109,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),X2),equivalent(X3,X2)),X)),true,ifeq(true,true,is_a_theorem(X),true),true) = true,
    inference(transitivity,[status(thm)],[c107,c108]) ).

cnf(c110,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),X2),equivalent(X3,X2)),X)),true,is_a_theorem(X),true) = true,
    inference(transitivity,[status(thm)],[c104,c109]) ).

cnf(c111,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)))),true,is_a_theorem(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),true) = true,
    inference(substitution,[status(thm)],[c110]) ).

cnf(c112,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),true) = true,
    inference(transitivity,[status(thm)],[c101,c111]) ).

cnf(c113,plain,
    is_a_theorem(equivalent(equivalent(equivalent(X6,equivalent(equivalent(equivalent(X6,X5),equivalent(X4,X5)),X4)),X3),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))) = true,
    inference(transitivity,[status(thm)],[c16,c112]) ).

cnf(c114,plain,
    is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),X5),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X4)),X5))) = true,
    inference(substitution,[status(thm)],[c113]) ).

cnf(c115,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),X5),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X4)),X5))),
    inference(symmetry,[status(thm)],[c114]) ).

cnf(c116,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(X5,X4),equivalent(X5,X4))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),X5),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X4)),X5))),true,is_a_theorem(equivalent(equivalent(X5,X4),equivalent(X5,X4))),true),
    inference(congruence,[status(thm)],[c115]) ).

cnf(c117,plain,
    ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2))),true,is_a_theorem(X),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2))),true,is_a_theorem(X),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c118,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2))),true,is_a_theorem(X),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2))),true,is_a_theorem(X),true),true),
    inference(symmetry,[status(thm)],[c117]) ).

cnf(c119,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X)),
    inference(symmetry,[status(thm)],[c42]) ).

cnf(c120,plain,
    ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2))),true,is_a_theorem(X),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2))),true,is_a_theorem(X),true),true),
    inference(congruence,[status(thm)],[c119]) ).

cnf(c121,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2)),X)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2))),true,is_a_theorem(X),true),true) = true,
    inference(substitution,[status(thm)],[c36]) ).

cnf(c122,plain,
    ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2))),true,is_a_theorem(X),true),true) = true,
    inference(transitivity,[status(thm)],[c120,c121]) ).

cnf(c123,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(X5,equivalent(equivalent(equivalent(X5,X4),equivalent(X3,X4)),X3)),X2),equivalent(X,X2))),true,is_a_theorem(X),true) = true,
    inference(transitivity,[status(thm)],[c118,c122]) ).

cnf(c124,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),X5),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X4)),X5))),true,is_a_theorem(equivalent(equivalent(X5,X4),equivalent(X5,X4))),true) = true,
    inference(substitution,[status(thm)],[c123]) ).

cnf(c125,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(X2,X),equivalent(X2,X))),true) = true,
    inference(transitivity,[status(thm)],[c116,c124]) ).

cnf(c126,plain,
    is_a_theorem(equivalent(equivalent(X2,X),equivalent(X2,X))) = true,
    inference(transitivity,[status(thm)],[c14,c125]) ).

cnf(c127,plain,
    true = is_a_theorem(equivalent(equivalent(X2,X),equivalent(X2,X))),
    inference(symmetry,[status(thm)],[c126]) ).

cnf(c128,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2)),X)),true) = ifeq(is_a_theorem(equivalent(equivalent(X4,X3),equivalent(X4,X3))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2)),X)),true),
    inference(congruence,[status(thm)],[c127]) ).

cnf(c129,plain,
    ifeq(is_a_theorem(equivalent(equivalent(X4,X3),equivalent(X4,X3))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2)),X)),true) = true,
    inference(substitution,[status(thm)],[c39]) ).

cnf(c130,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2)),X)),true) = true,
    inference(transitivity,[status(thm)],[c128,c129]) ).

cnf(c131,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2)),X)) = true,
    inference(transitivity,[status(thm)],[c12,c130]) ).

cnf(c132,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2)),X)),
    inference(symmetry,[status(thm)],[c131]) ).

cnf(c133,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(X,X2)),X)),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),X4),equivalent(X3,X4)),X3)),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(X,X2)),X)),true),
    inference(congruence,[status(thm)],[c132]) ).

cnf(c134,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),X4),equivalent(X3,X4)),X3)),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(X,X2)),X)),true) = true,
    inference(substitution,[status(thm)],[c39]) ).

cnf(c135,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(X,X2)),X)),true) = true,
    inference(transitivity,[status(thm)],[c133,c134]) ).

cnf(c136,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),X4),equivalent(X3,X4)),X3),X2),equivalent(X,X2)),X)) = true,
    inference(transitivity,[status(thm)],[c10,c135]) ).

cnf(c137,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2)),X),equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),X)),equivalent(X7,equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),X))),X7)) = true,
    inference(substitution,[status(thm)],[c136]) ).

cnf(c138,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2)),X),equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),X)),equivalent(X7,equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),X))),X7)),
    inference(symmetry,[status(thm)],[c137]) ).

cnf(c139,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(X7,equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),X)),X7)),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2)),X),equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),X)),equivalent(X7,equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),X))),X7)),true,is_a_theorem(equivalent(equivalent(X7,equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),X)),X7)),true),
    inference(congruence,[status(thm)],[c138]) ).

cnf(c140,plain,
    ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c141,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X)),true,is_a_theorem(equivalent(X2,X)),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),true),
    inference(symmetry,[status(thm)],[c140]) ).

cnf(c142,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X))),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c143,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X))),true),
    inference(symmetry,[status(thm)],[c142]) ).

cnf(c144,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),equivalent(X,X2)),X)),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),equivalent(X,X2)),X)),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c145,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),equivalent(X,X2)),X)) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),equivalent(X,X2)),X)),true),
    inference(symmetry,[status(thm)],[c144]) ).

cnf(c146,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,X3),equivalent(equivalent(equivalent(equivalent(X2,X),equivalent(X2,X)),X4),X3))),true) = is_a_theorem(equivalent(equivalent(X4,X3),equivalent(equivalent(equivalent(equivalent(X2,X),equivalent(X2,X)),X4),X3))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c147,plain,
    is_a_theorem(equivalent(equivalent(X4,X3),equivalent(equivalent(equivalent(equivalent(X2,X),equivalent(X2,X)),X4),X3))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,X3),equivalent(equivalent(equivalent(equivalent(X2,X),equivalent(X2,X)),X4),X3))),true),
    inference(symmetry,[status(thm)],[c146]) ).

cnf(c148,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X7,X6),equivalent(X7,X6)),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X4)),X3)),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X7,X6),equivalent(X7,X6)),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X4)),X3)),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c149,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X7,X6),equivalent(X7,X6)),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X4)),X3)),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X7,X6),equivalent(X7,X6)),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X4)),X3)),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),true),
    inference(symmetry,[status(thm)],[c148]) ).

cnf(c150,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),X),equivalent(X2,X))),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),X),equivalent(X2,X))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c151,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),X),equivalent(X2,X))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),X),equivalent(X2,X))),true),
    inference(symmetry,[status(thm)],[c150]) ).

cnf(c152,plain,
    ifeq(true,true,is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),X2),equivalent(X,X2)),X))),true) = is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),X2),equivalent(X,X2)),X))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c153,plain,
    is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),X2),equivalent(X,X2)),X))) = ifeq(true,true,is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),X2),equivalent(X,X2)),X))),true),
    inference(symmetry,[status(thm)],[c152]) ).

cnf(c154,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X))),true) = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X))),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c155,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X))) = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X))),true),
    inference(symmetry,[status(thm)],[c154]) ).

cnf(c156,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X)),X2)),equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X)))) = true,
    inference(substitution,[status(thm)],[c131]) ).

cnf(c157,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X)),X2)),equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X)))),
    inference(symmetry,[status(thm)],[c156]) ).

cnf(c158,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X)),X2)),equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X))),true),
    inference(congruence,[status(thm)],[c157]) ).

cnf(c159,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X)),X2)),equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X))),true) = true,
    inference(substitution,[status(thm)],[c55]) ).

cnf(c160,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X))),true) = true,
    inference(transitivity,[status(thm)],[c158,c159]) ).

cnf(c161,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X))) = true,
    inference(transitivity,[status(thm)],[c155,c160]) ).

cnf(c162,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),X2),equivalent(X,X2)),X)),equivalent(X5,equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),X2),equivalent(X,X2)),X)))) = true,
    inference(substitution,[status(thm)],[c161]) ).

cnf(c163,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),X2),equivalent(X,X2)),X)),equivalent(X5,equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),X2),equivalent(X,X2)),X)))),
    inference(symmetry,[status(thm)],[c162]) ).

cnf(c164,plain,
    ifeq(true,true,is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),X2),equivalent(X,X2)),X))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),X2),equivalent(X,X2)),X)),equivalent(X5,equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),X2),equivalent(X,X2)),X)))),true,is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),X2),equivalent(X,X2)),X))),true),
    inference(congruence,[status(thm)],[c163]) ).

cnf(c165,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),X2),equivalent(X,X2)),X)),equivalent(X5,equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),X2),equivalent(X,X2)),X)))),true,is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),X2),equivalent(X,X2)),X))),true) = true,
    inference(substitution,[status(thm)],[c55]) ).

cnf(c166,plain,
    ifeq(true,true,is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),X2),equivalent(X,X2)),X))),true) = true,
    inference(transitivity,[status(thm)],[c164,c165]) ).

cnf(c167,plain,
    is_a_theorem(equivalent(X5,equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X5),X2),equivalent(X,X2)),X))) = true,
    inference(transitivity,[status(thm)],[c153,c166]) ).

cnf(c168,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),X),equivalent(X2,X)),X2))) = true,
    inference(substitution,[status(thm)],[c167]) ).

cnf(c169,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),X),equivalent(X2,X)),X2))),
    inference(symmetry,[status(thm)],[c168]) ).

cnf(c170,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),X),equivalent(X2,X))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),X),equivalent(X2,X)),X2))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),X),equivalent(X2,X))),true),
    inference(congruence,[status(thm)],[c169]) ).

cnf(c171,plain,
    ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),true,is_a_theorem(X),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),true,is_a_theorem(X),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c172,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),true,is_a_theorem(X),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),true,is_a_theorem(X),true),true),
    inference(symmetry,[status(thm)],[c171]) ).

cnf(c173,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2)),X)),
    inference(symmetry,[status(thm)],[c131]) ).

cnf(c174,plain,
    ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),true,is_a_theorem(X),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2)),X)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),true,is_a_theorem(X),true),true),
    inference(congruence,[status(thm)],[c173]) ).

cnf(c175,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2)),X)),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),true,is_a_theorem(X),true),true) = true,
    inference(substitution,[status(thm)],[c36]) ).

cnf(c176,plain,
    ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),true,is_a_theorem(X),true),true) = true,
    inference(transitivity,[status(thm)],[c174,c175]) ).

cnf(c177,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),true,is_a_theorem(X),true) = true,
    inference(transitivity,[status(thm)],[c172,c176]) ).

cnf(c178,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),X),equivalent(X2,X)),X2))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),X),equivalent(X2,X))),true) = true,
    inference(substitution,[status(thm)],[c177]) ).

cnf(c179,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),X),equivalent(X2,X))),true) = true,
    inference(transitivity,[status(thm)],[c170,c178]) ).

cnf(c180,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2)),X),equivalent(X2,X))) = true,
    inference(transitivity,[status(thm)],[c151,c179]) ).

cnf(c181,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X7,X6),equivalent(X7,X6)),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X4)),X3)),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)))) = true,
    inference(substitution,[status(thm)],[c180]) ).

cnf(c182,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X7,X6),equivalent(X7,X6)),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X4)),X3)),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)))),
    inference(symmetry,[status(thm)],[c181]) ).

cnf(c183,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X7,X6),equivalent(X7,X6)),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X4)),X3)),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X7,X6),equivalent(X7,X6)),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X4)),X3)),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X7,X6),equivalent(X7,X6)),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X4)),X3)),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),true),
    inference(congruence,[status(thm)],[c182]) ).

cnf(c184,plain,
    ifeq(true,true,ifeq(is_a_theorem(equivalent(X4,equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)))),true,is_a_theorem(X4),true),true) = ifeq(is_a_theorem(equivalent(X4,equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)))),true,is_a_theorem(X4),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c185,plain,
    ifeq(is_a_theorem(equivalent(X4,equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)))),true,is_a_theorem(X4),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(X4,equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)))),true,is_a_theorem(X4),true),true),
    inference(symmetry,[status(thm)],[c184]) ).

cnf(c186,plain,
    true = is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),X4)),
    inference(symmetry,[status(thm)],[c98]) ).

cnf(c187,plain,
    ifeq(true,true,ifeq(is_a_theorem(equivalent(X4,equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)))),true,is_a_theorem(X4),true),true) = ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),X4)),true,ifeq(is_a_theorem(equivalent(X4,equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)))),true,is_a_theorem(X4),true),true),
    inference(congruence,[status(thm)],[c186]) ).

cnf(c188,plain,
    ifeq(is_a_theorem(equivalent(equivalent(X4,equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),X4)),true,ifeq(is_a_theorem(equivalent(X4,equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)))),true,is_a_theorem(X4),true),true) = true,
    inference(substitution,[status(thm)],[c36]) ).

cnf(c189,plain,
    ifeq(true,true,ifeq(is_a_theorem(equivalent(X4,equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)))),true,is_a_theorem(X4),true),true) = true,
    inference(transitivity,[status(thm)],[c187,c188]) ).

cnf(c190,plain,
    ifeq(is_a_theorem(equivalent(X4,equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)))),true,is_a_theorem(X4),true) = true,
    inference(transitivity,[status(thm)],[c185,c189]) ).

cnf(c191,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X7,X6),equivalent(X7,X6)),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X4)),X3)),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)),equivalent(X3,equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X7,X6),equivalent(X7,X6)),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X4)),X3)),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),true) = true,
    inference(substitution,[status(thm)],[c190]) ).

cnf(c192,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X7,X6),equivalent(X7,X6)),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X4)),X3)),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))),true) = true,
    inference(transitivity,[status(thm)],[c183,c191]) ).

cnf(c193,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X7,X6),equivalent(X7,X6)),equivalent(equivalent(equivalent(X5,X4),equivalent(X5,X4)),X3)),equivalent(equivalent(equivalent(X3,X2),equivalent(X,X2)),X))) = true,
    inference(transitivity,[status(thm)],[c149,c192]) ).

cnf(c194,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,X),equivalent(X2,X)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6)),equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6)))) = true,
    inference(substitution,[status(thm)],[c193]) ).

cnf(c195,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,X),equivalent(X2,X)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6)),equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6)))),
    inference(symmetry,[status(thm)],[c194]) ).

cnf(c196,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,X),equivalent(X2,X)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6)),equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6)))),true,is_a_theorem(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5))),true),
    inference(congruence,[status(thm)],[c195]) ).

cnf(c197,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,X),equivalent(X2,X)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6)),equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6)))),true,is_a_theorem(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5))),true) = true,
    inference(substitution,[status(thm)],[c177]) ).

cnf(c198,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(X4,X3),equivalent(equivalent(equivalent(equivalent(X2,X),equivalent(X2,X)),X4),X3))),true) = true,
    inference(transitivity,[status(thm)],[c196,c197]) ).

cnf(c199,plain,
    is_a_theorem(equivalent(equivalent(X4,X3),equivalent(equivalent(equivalent(equivalent(X2,X),equivalent(X2,X)),X4),X3))) = true,
    inference(transitivity,[status(thm)],[c147,c198]) ).

cnf(c200,plain,
    true = is_a_theorem(equivalent(equivalent(X4,X3),equivalent(equivalent(equivalent(equivalent(X2,X),equivalent(X2,X)),X4),X3))),
    inference(symmetry,[status(thm)],[c199]) ).

cnf(c201,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),equivalent(X,X2)),X)),true) = ifeq(is_a_theorem(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),equivalent(X,X2)),X)),true),
    inference(congruence,[status(thm)],[c200]) ).

cnf(c202,plain,
    ifeq(is_a_theorem(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),equivalent(X,X2)),X)),true) = true,
    inference(substitution,[status(thm)],[c39]) ).

cnf(c203,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),equivalent(X,X2)),X)),true) = true,
    inference(transitivity,[status(thm)],[c201,c202]) ).

cnf(c204,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),equivalent(X,X2)),X)) = true,
    inference(transitivity,[status(thm)],[c145,c203]) ).

cnf(c205,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X)),X2)),equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X)))) = true,
    inference(substitution,[status(thm)],[c204]) ).

cnf(c206,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X)),X2)),equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X)))),
    inference(symmetry,[status(thm)],[c205]) ).

cnf(c207,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X))),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X)),X2)),equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X))),true),
    inference(congruence,[status(thm)],[c206]) ).

cnf(c208,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X)),X2)),equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X)))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X))),true) = true,
    inference(substitution,[status(thm)],[c55]) ).

cnf(c209,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X))),true) = true,
    inference(transitivity,[status(thm)],[c207,c208]) ).

cnf(c210,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X))) = true,
    inference(transitivity,[status(thm)],[c143,c209]) ).

cnf(c211,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X))),
    inference(symmetry,[status(thm)],[c210]) ).

cnf(c212,plain,
    ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),true),
    inference(congruence,[status(thm)],[c211]) ).

cnf(c213,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X),equivalent(X2,X))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),true) = true,
    inference(substitution,[status(thm)],[c36]) ).

cnf(c214,plain,
    ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),true) = true,
    inference(transitivity,[status(thm)],[c212,c213]) ).

cnf(c215,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X6),X5)),X2),X)),true,is_a_theorem(equivalent(X2,X)),true) = true,
    inference(transitivity,[status(thm)],[c141,c214]) ).

cnf(c216,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2)),X),equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),X)),equivalent(X7,equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),X))),X7)),true,is_a_theorem(equivalent(equivalent(X7,equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),X)),X7)),true) = true,
    inference(substitution,[status(thm)],[c215]) ).

cnf(c217,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(X7,equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),X)),X7)),true) = true,
    inference(transitivity,[status(thm)],[c139,c216]) ).

cnf(c218,plain,
    is_a_theorem(equivalent(equivalent(X7,equivalent(equivalent(equivalent(equivalent(X6,X5),equivalent(X6,X5)),equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),equivalent(X,X2))),X)),X7)) = true,
    inference(transitivity,[status(thm)],[c8,c217]) ).

cnf(c219,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X),equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X)),equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X))),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X))),equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X))) = true,
    inference(substitution,[status(thm)],[c218]) ).

cnf(c220,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X),equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X)),equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X))),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X))),equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X))),
    inference(symmetry,[status(thm)],[c219]) ).

cnf(c221,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X)),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X),equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X)),equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X))),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X))),equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X)),true),
    inference(congruence,[status(thm)],[c220]) ).

cnf(c222,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X),equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X)),equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X))),equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X))),equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X))),true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X)),true) = true,
    inference(substitution,[status(thm)],[c55]) ).

cnf(c223,plain,
    ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X)),true) = true,
    inference(transitivity,[status(thm)],[c221,c222]) ).

cnf(c224,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X3,X2),equivalent(X3,X2)),X),X)) = true,
    inference(transitivity,[status(thm)],[c6,c223]) ).

cnf(c225,plain,
    is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,X),equivalent(X2,X)),X3),X3)) = true,
    inference(substitution,[status(thm)],[c224]) ).

cnf(c226,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,X),equivalent(X2,X)),X3),X3)),
    inference(symmetry,[status(thm)],[c225]) ).

cnf(c227,plain,
    ifeq(true,true,is_a_theorem(equivalent(X3,X3)),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,X),equivalent(X2,X)),X3),X3)),true,is_a_theorem(equivalent(X3,X3)),true),
    inference(congruence,[status(thm)],[c226]) ).

cnf(c228,plain,
    ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),
    inference(substitution,[status(thm)],[c2]) ).

cnf(c229,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X)),true,is_a_theorem(equivalent(X2,X)),true) = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),true),
    inference(symmetry,[status(thm)],[c228]) ).

cnf(c230,plain,
    true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X))),
    inference(symmetry,[status(thm)],[c161]) ).

cnf(c231,plain,
    ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),true) = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),true),
    inference(congruence,[status(thm)],[c230]) ).

cnf(c232,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X),equivalent(X2,X))),true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),true) = true,
    inference(substitution,[status(thm)],[c36]) ).

cnf(c233,plain,
    ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X)),true,is_a_theorem(equivalent(X2,X)),true),true) = true,
    inference(transitivity,[status(thm)],[c231,c232]) ).

cnf(c234,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X3),equivalent(X4,X3)),X2),X)),true,is_a_theorem(equivalent(X2,X)),true) = true,
    inference(transitivity,[status(thm)],[c229,c233]) ).

cnf(c235,plain,
    ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,X),equivalent(X2,X)),X3),X3)),true,is_a_theorem(equivalent(X3,X3)),true) = true,
    inference(substitution,[status(thm)],[c234]) ).

cnf(c236,plain,
    ifeq(true,true,is_a_theorem(equivalent(X,X)),true) = true,
    inference(transitivity,[status(thm)],[c227,c235]) ).

cnf(c237,plain,
    is_a_theorem(equivalent(X,X)) = true,
    inference(transitivity,[status(thm)],[c4,c236]) ).

cnf(c238,plain,
    is_a_theorem(equivalent(a,a)) = true,
    inference(substitution,[status(thm)],[c237]) ).

cnf(c239,plain,
    $false,
    inference(resolution,[status(thm)],[c1,c238]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL416-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04  % Command  : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37  % Computer : n010.cluster.edu
% 0.09/0.37  % Model    : x86_64 x86_64
% 0.09/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37  % Memory   : 8046.5625MB
% 0.09/0.37  % OS       : Linux 6.8.0-71-generic
% 0.09/0.37  % CPULimit : 300
% 0.09/0.37  % WCLimit  : 300
% 0.09/0.37  % DateTime : Sun Sep 27 15:41:16 UTC 2026
% 0.09/0.37  % CPUTime  : 
% 0.09/0.37  Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 156.87/20.29  Command-line arguments: --no-flatten-goal
% 156.87/20.29  
% 156.87/20.29  % SZS status Unsatisfiable
% 156.87/20.29  
% 157.70/20.33  % SZS output start CNFRefutation
% See solution above
% 160.89/20.72  
% 160.89/20.72  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------